Using a field-effect transistor (FET) configuration with solid Li-ion conductor (SIC) as gate dielectric, we have successfully tuned carrier density in FeSe0.5Te0.5 thin flakes, and the electronic phase diagram has been mapped out. It is found that electron doping controlled by SIC-FET leads to a suppression of the superconducting phase, and eventually gives rise to an insulating state in FeSe0.5Te0.5. During the gating process, the (001) peak in XRD patterns stays at the same position and no new diffraction peak emerges, indicating no evident Li + ions intercalation into the FeSe0.5Te0.5. It indicates that a systematic change of electronic properties in FeSe0.5Te0.5 arises from the electrostatic doping induced by the accumulation of Li + ions at the interface between FeSe0.5Te0.5 and solid ion conductor in the devices. It is striking that these findings are drastically different from the observation in FeSe thin flakes using the same SIC-FET, in which Tc is enhanced from 8 K to larger than 40 K, then the system goes into an insulating phase accompanied by structural transitions.