A power system network is an interconnection of large number of generating stations, long transmission lines, and distribution network loads. This an interconnected power system network will face to different instability problem. Power system instability problem is the occurred by the existence of low frequency oscillation in the power system network. Low frequency oscillation may be created by small signal disturbance, such as change in the load, the use of high gain exciters, the use of high voltage direct current converters with negative damping and connection of poorly tuned generator excitations. These small disturbance lead to steady increase or decrease in generator rotor angle caused by the lack of synchronizing torque, or to the rotor oscillation of increasing amplitude due to the lack of sufficient damping torque. The fundamental factor in this problem is the way in which the power outputs of synchronous generator and the load differ as their rotors oscillate. This work is concerned on minimizing oscillation of a power system by using STATCOM and fuzzy logic controller. The study is carried out on the single machine infinite bus test system and taking standard data from the literature. The application of fuzzy logic controller is investigated by means of simulation studies on a model of single machine infinite bus system with its linearized equations using MATLAB simulink. Speed deviation and acceleration of the synchronous machine are chosen as the input signals for the fuzzy logic controller to enhance dynamic stability of a power system. The base case of the system response and the proposed system with constant field voltage, excitation, power system stabilizer, fuzzy logic controller, and synchronous compensator are simulated. The result of 25% input mechanical power change of speed, rotor angle, and electrical torque deviation response versus time are obtained. Simulation result shows that the oscillation of rotor angle response with STATCOM and fuzzy logic controller for single machine infinite bus system is damped at 0.5second with amplitude of 0.5pu. Whereas, the oscillation of the rotor angle response with conventional power system stabilizer is damped at 3.0second with amplitude of 0.5pu. In general, using STATCOM with fuzzy logic controller provides good damping of local mode oscillation, low overshoot and less settling time response.