The magnetic and magnetocaloric properties of Ni45Mn43CoSn11 have been investigated using heat capacity measurements and magnetization with hydrostatic pressure applications. A shift in the martensitic transition temperature by 40 K to higher temperatures was observed with application of pressure P = 1.06 GPa. The magnetic entropy changes significantly increases from 24 to 42 J/kgK at pressure of 0.73 GPa. A large adiabatic temperature change of 4 K was found from specific heat measurements. Also, the density of states and Debye temperature has been estimated from heat capacity measurements. The mixed effects of pressure and magnetic field on the transition temperature are discussed.