We have carried out the specific heat and electric resistivity measurements of the chalcogenide-spinel compound CuRh2S4 under the hydrostatic pressures up to 8.0 GPa, and found out the pressure induced superconductor-insulator (SI) transition at PSI in between 5.0 and 5.6 GPa. The value of superconducting transition temperature Tc, which is 4.7 K at ambient pressure, increases up to 6.4 K at 4.0 GPa and turns to decrease with pressurization. With further pressurization, the abrupt loss of Tc occurs at PSI and the system becomes an insulator.