In this paper, an intelligent controller is proposed to control a static synchronous series compensator (SSSC) in order to mitigate subsynchronous resonance (SSR) oscillations in a power system. This intelligent controller is an adaptive self-tuning PID controller. To train the PID controller, the gradient descent method is employed where the learning rate is adapted in every iteration in order to accelerate the speed of convergence. This control scheme also requires a wavelet neural network (WNN) to identify the controlled system dynamic. To update the parameters of WNN, the gradient descent (GD) along with the adaptive learning rates derived by the Lyapunov method is used. The computer simulations are used to show the ability of the proposed controller. In addition, the performance of the proposed controller is compared with another self-tuning PID controller. The results demonstrate that the proposed controller has a successful performance in minimizing the SSR.