We report upon the effect of hydrostatic pressure on the martensitic transition, magnetic properties, and magnetic entropy change in Ni50-xMn37 + xSn13 (x = 2, 3) Heusler alloys. The application of pressure has significantly shifted the martensitic transition temperature to higher values. A large rate of change of the martensitic transition with a pressure of ∼3.1 K/kbar has been obtained for the x = 2 alloy, whereas the Curie temperature changes marginally with pressure (∼0.3 K/kbar). Magnetization of both the austenite and martensite phases decreases with an increase of pressure. The maximum magnetic entropy change of 34 J kg-1K-1 at ambient pressure and 22.5 J kg-1K-1 at 8 kbar was observed around the martensitic transition temperature for the x = 3 alloy.