Pressure-induced phase transitions in a monoclinically distorted LiNbO3-type CuNbO3 with triangularly coordinated Cu and octahedrally coordinated Nb were experimentally and computationally investigated. Phase transitions into GdFeO3-type or NaIO3-type structures generally observed in LiNbO3-type compounds below 30 GPa were not detected in CuNbO3 even at the maximum experimental pressure, 32.4 GPa. Our density functional theory calculations revealed that the phase transition is suppressed by the preference for the CuO3 triangular coordination environment, which reduces the total internal energy. This study clarifies that the change in the coordination environment of given ions can affect the pressure-induced phase transition.