We have demonstrated a pressure-induced phase transition from a low-Tc phase to a high-Tc phase in a single crystal of the superconductor LaO0.5F0.5BiSe2. The high-Tc phase appears at 2.16 GPa and the maximum superconducting transition temperature (Tc) is observed at 6.7 K under 2.44 GPa. Although the anisotropy ({gamma}) for the low-Tc phase is estimated to be 20, it is reduced by around half (9.3) in the high-Tc phase. This tendency is the same for the BiS2 system. The Tc of LaO0.5F0.5BiSe2 has continued to increase up to the maximum pressure of this study (2.44 GPa). Therefore applied further pressure has the potential to induce a much higher Tc in this system.