Thermodynamic properties of two organic superconductors, κ-(BEDT-TTF)2 Ag(CN)2H2O, κ-(BEDT-TTF)2 Cu(NCS)2 are studied by the ac-modulation technique under pressures and with magnetic fields. The superconducting transition temperatures of these complexes are 5 K and 9.6 K, respectively. The former complex shows a thermal anomaly related to the superconducting phase transition around 5 K at ambient pressure and its disappearance under pressure of 4 kbar is confirmed. On the other hand, the latter complex shows a systematic pressure dependence of the superconducting transition temperature (Tc). The suppression of the superconductive phase of both organic superconductors by applying the pressure is consistent with the feature of the two-dimensional strongly correlated electron system of the dimer-Mott organic salts.