Medicare Hospital Reimbursement Reform Act - Amends title XVIII (Medicare) of the Social Security Act to provide an alternative hospital reimbursement system. Authorizes a State and certain legal entities to apply to have hospitals within a State or geographic area reimbursed under the alternative system. Requires a State using an alternative method to assure that under the alternative method: (1) hospital expenditures under Medicare and Medicaid (title XIX of the Act) will not be greater than if the alternative system was not in effect; and (2) there will not be a significant reduction of or refusal to admit specified classes of patients to hospitals.

Permits the States and certain legal entities to apply for a grant to aid in establishing the alternative system.