Abstarct: Low frequency oscillations (LFO) in power system occur usually because of lack of damping torque to overcome disturbances in power system such as changes in mechanical power. Traditionally, power system stabilizers (PSS) are being used to damp these oscillations. Unified Power Flow Controller (UPFC) is a well-known FACTS device that can control power flow in transmission lines. It can be also replaced by PSS to damp low frequency oscillations effectively through direct control of voltage and power. In this thesis a linearized Heffron-Philips model of a (Single Machine–Infinite Bus) power system with a unified power flow controller is developed. The designed fuzzy-baxsed UPFC controller adjusts four UPFC inputs by appropriately processing of the input error signal, and provides an efficient damping. The results of the simulation show that the UPFC with fuzzy-baxsed controllers is more effective in damping LFO compared to UPFC with PID controllers. Also, using fuzzy c-means clustering method proposed fuzzy controllers have been optimized. Simulation results for these optimized fuzzy controllers show that oscillations have been damped.