The effect of pressure on the magnetic and the magnetocaloric (MC) properties around the martensitic transformation temperature in NiCoMnSb Heusler alloy has been studied. The martensitic transition temperature has significantly shifted to higher temperatures with pressure, whereas the trend is opposite with the application of applied magnetic field. The maximum magnetic entropy change around the martensitic transition temperature for Ni(45)Co(5)Mn(38)Sb(12) is 41.4 J/kg K at the ambient pressure, whereas it is 33 J/kg K at 8.5 kbar. We find that by adjusting the Co concentration and applying suitable pressure, NiCoMnSb system can be tuned to achieve giant MC effect spread over a large temperature span around the room temperature, thereby making it a potential magnetic refrigerant material for applications.1065