Sub-Synchronous Resonance (SSR) is an adverse oscillation that may happen when steam turbine-generator is connected to a long transmission line system which compensated with series capacitor. If this oscillation is not damped completely, the operation of the turbine-generator shaft will be deteriorated, that causes serious shaft failure. The main scope of this paper is to design a Fuzzy Logic Damping Controller (FLDC) for Static VAR Compensator (SVC) to suppress the SSR. It is widely accepted that, the main duty of SVC in power system is to regulate the bus voltage. The novel FLDC is designed and granted to conventional controller of SVC in order to alleviate the SSR. For analyzing the designed controller, a summarized prony analysis associated with time domain simulation is also clarified. Simulation results are carried out with MATLAB/SIMULINK in order to prove the capability of proposed controller in power system stability. Also, a comparison between suggested controller and conventional damping controller (CDC) is performed that demonstrates the superior operation of FLDC toward its counterpart, CDC.