Fully superconducting generator (FSG) is one of the promising applications of superconductors in electric power sector. Meanwhile, transient stability of FSG is an important issue in developing this new machine. An approach is suggested in this paper for the design of a fuzzy logic governor controller (FLC) as a possible mean to improve the FSG stability under transient conditions. In this approach, unsymmetrical nonlinear membership functions are used, while number of FLC parameters to be properly designed is 15 parameters, including scaling factors for input and output variables along with widths and centers of fuzzy sets of input variables. A genetic algorithm is used to optimally choose all these parameters. Simulation results show that the proposed FLC leads to a significant improvement in the transient stability and performance of a FSG connected to an infinite-bus.