The result is a difference in "risk scores" between equivalent patient populations based on a difference in methodology between MA and fee-for-service Medicare.
The GAO's conclusion applies to CMS's work in adjusting for this difference, which auditors said was inadequate.
"CMS's adjustment does not accurately account for the differences in treatment and diagnostic coding" between Medicare Advantage and traditional Medicare, the office wrote.
Overpayments may have been as high as $5.1 billion between 2010 and 2012, the report added.
It urged Medicare officials to use more information, such as additional beneficiary characteristics, to make its risk-score adjustments.
The report comes as the health insurance industry aggressively pushes back against proposed cuts to Medicare Advantage from the Obama administration.
The Health and Human Services Department said Feb. 15 that MA plans will face a 2.2 percent payment cut in 2014 on top of reductions ordered by the Affordable Care Act.
Health insurers argue the cuts will hurt the plans' poor and minority beneficiaries, who report satisfaction with their coverage.
But Democrats on Capitol Hill used Monday's report to argue that MA cuts are appropriate.
"While CMS has continued to strengthen the Medicare Advantage program, today’s GAO report provides evidence that there is yet more to do," said Rep. Henry Waxman (Calif.), top Democrat on the House Energy and Commerce Committee, in a statement.
"One of the best ways to protect Medicare for generations to come is to ensure that the program isn’t overspending for care and services."