
514 F.3d 818 (2008)
UNITED STATES of America, Plaintiff-Appellee,
v.
Nathan Allen HUFF, Defendant-Appellant.
No. 07-1500.
United States Court of Appeals, Eighth Circuit.
Submitted: October 16, 2007.
Filed: January 30, 2008.
*819 Troy K. Stabenow, Asst. Fed. Public Defender, Jefferson City, MO, argued (Raymond C. Conrad, Jr., Fed. Public Defender, Kansas City, MO, on the brief), for appellant,
Philip M. Koppe, Asst. U.S. Atty., Kansas City, MO, argued (Bradley. J. Schlozman, U.S. Atty., Kansas City, MO, Lawrence E. Miller, Asst. U.S. Atty., Jefferson City, MO, on the brief), for appellee.
Before BYE, BOWMAN, and SMITH, Circuit Judges.
BYE, Circuit Judge.
Nathan Allen Huff appeals the thirty-seven month sentence imposed following his guilty plea to being a felon in possession of a firearm. Huff argues the district court improperly applied a presumption of reasonableness to the applicable guidelines range. We vacate Huff's sentence and remand for resentencing.

I
On August 29, 2006, Nathan Allen Huff pleaded guilty to being a felon in possession of a firearm, in violation of 18 U.S.C. § 921(g)(1). The presentence investigation report ("PSR") concluded Huff's advisory guidelines range was 108 to 135 months, based on a total offense level of 20 and a criminal history category of V. The total offense level of 20 included: (1) a base offense level of 14; (2) a two-level enhancement under U.S.S.G. § 2K2.1(b)(4) because the firearm Huff possessed had previously been reported stolen; and (3) a four-level enhancement under U.S.S.G. § 2K2.1(b)(6) because Huff possessed the firearm in conjunction with another felony offense.
At the sentencing hearing, Huff objected to the four-level enhancement under U.S.S.G. § 21(2.1(b)(6).[1] The district court overruled Huff's objection and found, by a preponderance of the evidence, Huff had illegally exhibited a firearm, thus warranting the four-level enhancement. Additionally, Huff moved for a downward departure under U.S.S.G. § 5K2.10, based on the victim's contribution to the offense. The district court granted Huff's motion and gave him a two-level downward departure. Huff requested an additional downward departure or variance based on his past history of extraordinary abuse and the way it affected his emotional state at the time of the offense. The district court declined to grant the departure or variance, noting current Eighth Circuit law, namely United States v. Claiborne, 439 F.3d 479 (8th Cir.2006), overruled by Gall v. United States, ___ U.S. ___, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007), precluded a variance.
After applying a three-level reduction for acceptance of responsibility, the district *820 court determined Huff's total offense level was 15 and his criminal history category was V, resulting in a guidelines range of thirty-seven to forty-six months. The district court then sentenced Huff at the low end of the applicable range to thirty-seven months.
This appeal followed. On appeal, Huff challenges the basis for the court's decision not to impose a downward variance.

II
This court reviews a district court's sentence determination under an abuse-of-discretion standard. The United States Supreme Court recently clarified the scope of our review;
[T]he appellate court must first ensure that the district court committed no significant procedural error, such as failing to calculate (or improperly calculating) the Guidelines range, treating the Guidelines as mandatory, failing to consider the § 3553(a) factors, selecting a sentence based on clearly erroneous facts, or failing to adequately explain the chosen sentenceincluding an explanation for any deviation from the Guidelines range. Assuming that the district court's sentencing decision is procedurally sound, the appellate court should then consider the substantive reasonableness of the sentence imposed under an abuse-of-discretion standard.
Gall, 128 S.Ct. at 597. See also Koon v. United States, 518 U.S. 81, 100, 116 S.Ct. 2035, 135 L.Ed.2d 392 (1996) ("The abuse-of-discretion standard includes review to determine that the discretion was not guided by erroneous legal conclusions.").
According to Huff, the record demonstrates the district court interpreted this court's binding precedent to require application of a presumption of reasonableness to the applicable guidelines range and to preclude a variance in the absence of extraordinary circumstances. As the Supreme Court made clear in Rita v. United States, ___ U.S. ___, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007), the presumption of reasonableness is an appellate presumption and "the sentencing court does not enjoy the benefit of a legal presumption that the Guidelines sentence should apply." Id. at 2465. See also United States v. Wilms, 495 F.3d 277, 282 (6th Cir.2007) (reversing and remanding defendant's sentence due to the district court's imposition of a presumption of reasonableness in violation of Rita); United States v. Foreman, 436 F.3d 638, 644 n. 1 (6th Cir.2006) ("[A] district court's job is not to impose a `reasonable' sentence. Rather, a district court's mandate is to impose `a sentence sufficient, but not greater than necessary, to comply with the purposes' of section 3553(a)(2). Reasonableness is the appellate standard of review in judging whether a district court has accomplished its task.").
The record in this case makes clear, based on the presumption of reasonableness, the district court did not believe it had the discretion to vary from the applicable guidelines range. In denying Huff's request for a variance, the district court stated: "I have no idea what's going to happen with Claiborne. But given the current state of the Eighth Circuit, I don't see how I can do a variance." The district court further explained: "I might have departed more in this case but for the Eighth Circuit precedent in the Claiborne case. And if, in fact, that case were to be overturned on appeal, then I would hope that we would have an opportunity to review this sentence . . . I would have given him less of a sentence if I thought that I had the ability to do so." Sent. Tr. at 73, 74, 75.
In light of Rita, the district court's application of a presumption of reasonableness was an abuse of discretion. The district *821 court imposed the sentence not as a result of the district court's assessment of the relevant factors and determination of the minimally adequate sentence, as required by § 3553(a), but as a direct consequence of the court's incorrect conclusion it was bound by Eighth Circuit precedent to accord the guidelines range presumptive weight. See Koon, 518 U.S. at 100, 116 S.Ct. 2035 ("A district court by definition abuses its discretion when it makes an error of law.") (citing Cooter & Gell v. Hartmarx Corp. 496 U.S. 384, 403-05, 110 S.Ct. 2447, 110 L.Ed.2d 359 (1990)).
Further, we do not believe this error was harmless.[2] The government bears the burden of proving the district court's error was harmless, and must show that no "grave doubt" exists as to whether the error substantially influenced the outcome of the proceedings. United States v. Cullen, 432 F.3d 903, 905-06 (8th Cir.2006) (citations omitted). The record makes clear had the district court properly exercised its discretion, it likely would have granted Huff's request for a variance. Sent. Tr. at 73, 74, 75 ("[I]f, in fact, that case were to be overturned on appeal, then I would hope that we would have an opportunity to review this sentence . . . I would have given him less of a sentence if I thought that I had the ability to do so."). Given the record, we conclude the error substantially influenced the outcome of the proceedings and, therefore, was not harmless.

III
Accordingly, we vacate Huff's sentence and remand for resentencing consistent with this opinion.
NOTES
[1]  Huff did not object to the two-level enhancement under U.S.S.G. § 21(2.1(b)(5).
[2]  We find, and the government does not disagree, Huff raised a timely objection during sentencing and, therefore, preserved his challenge.
