We report a study of the effect of hydrostatic pressure on the magnetocaloric effect in a La _0.69 Ca _0.31 Mn O ₃ single crystal. The single crystal exhibits a much larger magnetic entropy change (ΔS_m) than the corresponding polycrystalline samples, reaching 5.2 J / kg K and 8.5 J / kg K for a magnetic field variation of 1 T and 5 T , respectively. Under hydrostatic pressure, the peak position of ΔS_m significantly moves to higher temperatures due to the shift of the magnetic phase transition, from 213.5 K under ambient pressure up to 236.5 K under a pressure of 1.1 GPa , while the maximum value of ΔS_m remains nearly the same. These exceptional results demonstrate that the magnetocaloric effect in magnetic materials with strong spin-lattice coupling can be effectively tuned by pressure.