The invention relates to the alfalfa variety designated R513M225S. Provided by the invention are the seeds, plants and derivatives of the alfalfa variety R513M225S. Also provided by the invention are tissue cultures of the alfalfa variety R513M225S and the plants regenerated therefrom. Still further provided by the invention are methods for producing alfalfa plants by crossing the alfalfa variety R513M225S with itself or another alfalfa variety and plants produced by such methods.
