Unified Power Flow Controller (UPFC) is one of the most effective Flexible AC Transmission Systems (FACTS) devices for controlling power flow and improving stability of power system. To achieve the functionality of UPFC, a proper and sufficient control system should be designed for this device. Our research proposes a Fuzzy Logic control approach to control UPFC. The proposed control scheme is used to control and coordinate voltage and phase angle signals of Voltage Source Converters (VSCs) of UPFC, where these two signals are used to control active and reactive power flow in transmission line. To validate the proposed control scheme, a single-machine double line infinite bus power system equipped with UPFC is modeled using PSCAD/EMTDC software package. Three phase fault with ground case is simulated and investigated under the proposed controller. The modeling and simulation results show the effectiveness of the UPFC under the proposed control scheme for improving power system stability under the three phase fault case. The results also show the robustness and superiority of the proposed controller compared to conventional PI controller as well as it guarantees the closed-loop stability system and has a good tracking behavior.