Medicare HMO Sanction Reform and Anti-Fraud and Abuse Act of 1991 - Amends title XVIII (Medicare) of the Social Security Act to authorize the Secretary of Health and Human Services to terminate the risk-sharing contract of, or impose intermediate sanctions (including civil money penalties and the suspension of the enrollment of individuals) against, any participating health maintenance organization (HMO) that: (1) is carrying out the contract in a manner inconsistent with efficient and effective administration; (2) is operating in a manner that is not in the best interests of covered individuals; or (3) does not meet other specified contract requirements. Sets forth requirements for investigation and compliance procedures for terminating a contract or imposing such sanctions.

Requires written agreements between participating HMOs with risk-sharing contracts and entities providing peer review services with respect to services provided by HMOs. Requires the Secretary to develop a model of such an agreement.

Requires the Comptroller General to conduct a study and report to specified congressional committees on compliance costs incurred by such HMOs with respect to entering into such a written agreement.

Amends title XI of the Social Security Act to subject to civil monetary penalties any person that: (1) transfers anything for less than fair market value to (or for the benefit of) a beneficiary in order to influence the individual to receive from a particular provider, practitioner, or supplier a covered item or service for which payment may be made under Medicare or Medicaid (title XIX of the Social Security Act); or (2) pays an incentive to induce an employee to encourage individuals to seek or obtain such an item or service where the amount of the incentive is in proportion to the encouraging activities of the employee.