In recent years, FACTS devices are recognized as one of the most effective ways to improve power system operation controllability and increase power transfer limits. Gate-Controlled Series Capacitor (GCSC) is one of these FACTS devices which is installed in series with the transmission line. In turn, the supplementary controllers are applied to FACTS technology to boost the produced damping torque. Recently, evolutionary and meta-heuristic algorithms have been extensively used to optimize the parameters of damping controllers. In this paper, on the basis of the linearized Heffron-Phillips model of a single machine power system with GCSC, the Particle Swarm Optimization (PSO) algorithm is used to design a lead-lag damping controller for the GCSC. A time domain and an undamped eigenvalue based objective functions are employed as two different fitness. To verify the robustness of the proposed controllers, various operating conditions are simulated due to a severe disturbance. Observing and analyzing the results reveals appropriate performance of this controller in damping the power system oscillations and enhancing the dynamic stability. Moreover, the undamped eigenvalue based fitness is superior to time domain based one.