The invention relates to the alfalfa variety designated 510M374. Provided by the invention are the seeds, plants and derivatives of the alfalfa variety 510M374. Also provided by the invention are tissue cultures of the alfalfa variety 510M374 and the plants regenerated therefrom. Still further provided by the invention are methods for producing alfalfa plants by crossing the alfalfa variety 510M374 with itself or another alfalfa variety and plants produced by such methods.