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A long transmission line needs controllable series as well as shunt compensation for power flow control and voltage regulation. In this paper, series fixed capacitive compensation and shunt compensation provided by a Static VAR Compensator (SVC) installed at the transmission line are considered. It is possible to damp Sub-Synchronous Resonance (SSR) caused by series capacitors with the help of an auxiliary SSR damping controller on SVC. In this work, two novel control methods for damping SSR is added to the SVC main control in order to demonstrate the SSR damping capability of SVC. The control methods are presented, namely: Fuzzy Logic Damping Controller (FLDC) and Adaptive Neuro-Fuzzy Inference System (ANFIS) controller. The ANFIS constructions were trained utilizing the generated database by the FLC of the SVC. The simulation results prove that ANFIS controller is found to be robust to fault type and change in operating situations. The Fast Fourier Transform (FFT) is carried out in order to evaluate the effect of TCSC based ANFIS controller in damping SSR and LFO. The study system was adopted from the IEEE Second Benchmark Model (ISBM) by installing the SVC. The MATLAB/Simulink software program was used to verify the effectiveness of each control method.