Both magnetic-field-induced reverse martensitic transformation (MFIRMT) and a high working temperature are crucial for the application of Ni-Mn-Sn magnetic shape memory alloys. Here, by first-principles calculations, we demonstrate that the substitution of Cu for Sn is effective not only in enhancing the MFIRMT but also in increasing martensitic transformation, which is advantageous for its application. Large magnetization difference (∆M) in Ni-Mn-Sn alloy is achieved by Cu doping, which arises from the enhancement of magnetization of austenite due to the change of Mn-Mn interaction from anti-ferromagnetism to ferromagnetism. This directly leads to the enhancement of MFIRMT. Meanwhile, the martensitic transformation shifts to higher temperature, owing to the energy difference between the austenite L2 1 structure and the tetragonal martensite L1 0 structure increases by Cu doping. The results provide the theoretical data and the direction for developing a high temperature magnetic-field-induced shape memory alloy with large ∆M in the Ni-Mn-Sn Heusler alloy system.