Films of the Mn-based tetragonal Heusler-like alloys, such as Mn-Ga, exhibit a large perpendicular magnetic anisotropy (PMA), small damping constant, small saturation magnetization and large spin polarizations. These properties are attractive for the application to the next generation high density spin-transfer-torque (STT) magnetic random access memory (STT-MRAM). We reviewed the structure, magnetic properties and Gilbert damping of the alloy¯lms with large PMA, and the current status of research on tunnel magnetoresistance (TMR) in perpendicular magnetic tunnel junctions (p-MTJs) based on Mn-based tetragonal Heusler-like alloy electrode, and also discuss the issues for the application of those to STT-MRAM.