An important aspect in developing superconducting generator (SCG) concerns stability following a major system disturbance. This paper presents a method for enhancing stability of a SCG connected to an infinite-bus system using one of FACTS devices. In this method, a static VAR compensator (SVC)-based stabilizer is designed in coordination with a governor controller (GC) to effectively damp the mechanical oscillations which arise in the system when subjected to a disturbance. A time response-based objective function is defined and the design problem of SVC-based stabilizer and GC is formulated into an optimization problem. Particle swarm optimization (PSO) technique is employed to find out an optimal set of parameters for SVC-based stabilizer and GC. Simulation results, damping torque analysis, and small signal analysis show that the proposed PSO-based control scheme provides more damping to the SCG, and enhances its stability over a range of operating conditions.