By using a hydrostatic pressure, we have successfully tuned the ground state and superconductivity in LaO0.5F0.5BiSe2 single crystals. It is found that, with the increase of pressure, the original superconducting phase with Tc ∼ 3.5 K can be tuned to a state with lower Tc, and then a new superconducting phase with Tc ∼ 6.5 K emerges. Accompanied by this crossover, the ground state is switched from a semiconducting state to a metallic one. Accordingly, the normal state resistivity also shows a nonmonotonic change with the external pressure. Furthermore, by applying a magnetic field, the new superconducting state under pressure with Tc ∼ 6.5 K is suppressed, and the normal state reveals a weak semiconducting feature again. These results illustrate a non-trivial relationship between the normal state property and superconductivity in this newly discovered superconducting system.