We have measured heat capacities of organic superconductor κ-(BEDT-TTF)2Cu(NCS)2 under several pressures. This compound shows superconductive transition around 10 K, and we have detected an anomaly of the superconductive transition at about 9.4 K under ambient pressure. The transition temperature shifts to lower temperatures under 2.5 kbar and 4 kbar. Simultaneously, the peak-size changes from large one to small one and the peak-shape changes from sharp one to broader one with the decrease of transition temperature. The differences of peak-size and peak-shape may be related to stability of superconductivity in the κ-(BEDT-TTF)2X phase diagram. We think these changes imply superconducting phase changes from strong coupling regime to weak coupling regime