LiOsO3 is a strongly correlated metal that undergoes a nonpolar to polar transition at the critical temperature (Ts) of 140 K. Complementary to previous studies of structure, Raman, and resistivity under high pressure (P), here we map out a complete pressure evolution of Ts(P) via high-pressure resistance measurements up to 18.5 GPa by using a low-temperature multianvil apparatus. Our results show that Ts(P) first increases linearly with pressure at a large slope as reported and then levels off gradually at pressures above 10 GPa when approaching room temperature (295 K). Interestingly, we find that the resistance R(T) of LiOsO3 at 18.5 GPa in the polar R3c phase exhibits a distinct temperature profile in comparison with those at lower pressures, signaling the possible occurrence of pressure-driven new electronic phase. The critical pressure for this transition is determined to be Pc = 16.8(1) GPa based on the pressure-dependent resistance measurement at room temperature.