Thermodynamic properties of an organic superconductor of κ-[(BEDT-TTF)1−x(BEDSe-TTF)x]2Cu[N(CN)2]Br (x ~ 0.1) have been studied by the ac-modulation technique under pressures and with magnetic fields. The superconductive transition temperature of x = 0 salt (11.6 K) shifts to lower temperature with the increase of x. Over x ~ 0.33, the superconductivity is suppressed. Using the high-pressure calorimetry cell, we have observed a thermal anomaly around 6 K at ambient pressure. The suppression of the superconductivity by magnetic fields suggests that the observed peak is associated with the superconductive transition. Upon pressurize to 3 kbar, a thermal anomaly related to the superconductive transition was observed around 4.7 K. The decrease of transition temperature Tc suggests that the superconductive phase has suppressed by applying the pressure.