The martensite transformation (MT) behavior and magneto-caloric effect (MCE) in polycrystalline Ni44Mn36In14Co6 alloy were tuned by doping the fifth element, 2 at.% Cu. The process of heat-induced MT was observed by in-situ scanning electron microscopy and the magnetic-field-induced reversible MT was confirmed by magnetic properties test near room temperature. A large magnetization change (ΔM, 111emu/g), relatively high sensitivity to magnetic fields (3.8 K/T), a large MCE (33.7J kg−1 K−1) and the two-way magnetic-field-induced transformation were attained around the MT. The combination properties in the Ni42Mn36In14Co6Cu2 alloy are instructive for the development of high-performance magnetic refrigeration and intelligent actuator materials.