According to the analysis results for the principle of electrical discharge machining （EDM）and feed system, it is acquired that one of the important factors affecting the quality of microhole machining is discharge gap. So reliably control of discharge gap is the key to improve the microhole machining quality and efficiency. In order to better control the discharge gap and analyze the law of control of discharge gap, the fuzzy controller for EDM control system was designed by applying fuzzy theory. Moreover by taking advantage of Lyapunov theory of stability, the stability of control system was analyzed and verified. The results show the feasibility and stability of system.