Although using a series compensation technique in a long transmission line effectively increases the transmittable power; it may cause a sub-synchronous resonance (SSR) phenomenon. Gate-controlled series capacitor (GCSC) is an effective method for SSR damping by controlling the turn-off angle. In the previous studies, a constant supplementary damping controller (SDC) was used for controlling the turn-off angle, which can mitigate the SSR phenomenon. However, these methods can not capture the maximum transmittable power at different operating points. In this paper, a fuzzy logic controller (FLC) is proposed to compute the gain of SDC based on the wind speed and the error between the measured and reference line currents for transferring as much power as possible and damping the SSR phenomenon simultaneously. Using the MATLAB/SIMULINK program, the proposed method is tested at different operating points to validate its effectiveness and robustness. Compared to the traditional method (constant SDC), the maximum transmittable power, as well as SSR damping, is achieved in all studied cases by the proposed method (variable SDC).