Rebuilding the Economy and Limiting the Impacts of Expected Flooding Act of 2011 or the RELIEF Act of 2011 - Authorizes the Administrator of the Federal Emergency Management Agency (FEMA) to make grants to local governments for flood mitigation projects. Directs the Administrator to give priority to: (1) projects that will resolve the greatest safety and property hazards, and (2) projects with significant capacities for job creation. Allows the Administrator to provide such grant assistance to a local government without regard to its eligibility to receive financial assistance for the project under another federal program.