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This paper analyzes the effect of the fuzzy logic- controlled superconducting magnetic energy storage (SMES) on damping turbine-generator shaft torsional oscillations during unsuccessful reclosing of circuit breakers. The control scheme of SMES is based on a PWM voltage source converter (VSC) and a two-quadrant DC-DC chopper using gate-turn-off (GTO) thyristor. Simulation results of both balanced and unbalanced faults in a single machine connected to an infinite bus system show that the proposed fuzzy logic-controlled SMES is effective in damping shaft torsional oscillations of synchronous generators during unsuccessful reclosing of circuit breakers.