In the present work, we report the dependence of magnetization on hydrostatic pressure for the non-stoichiometric Ni58.3Mn17.1Ga24.6 alloy, which undergoes the transformation from a paramagnetic austenite to a ferromagnetic martensite near room temperature. It is found that the application of pressure can push the martensitic transformation (MT) to a higher temperature at a rate of 4 K GPa(-1). Considering the change of phase fraction under the isothermal condition caused by pressure-induced MT, we develop an indirect method based on magnetic data measured under various pressures to determine the barocaloric effect (BCE) for the studied alloy. When the change of the applied hydrostatic pressure reaches 1.05 GPa, the maximum isothermal entropy change is calculated to be about -13.6 J kg(-1) K-1, yielding a value of 2.8 K for the adiabatic temperature change near room temperature. These values are comparable to those obtained in many alloys of the same series by using superconducting magnets. Such a considerable BCE can be attributed to the fact that the MT can be driven more easily by the pressure-induced crystallographic change than by the magnetic field-induced spin-lattice coupling.