In order to meet the requirements of machining accuracy of CNC machine tools,a fractional order PID controller with adaptive step size based on firefly algorithm(ASGSO-FOPID) was designed to solve the nonlinear problems of disturbance,friction,variable load and inertia torque in the feed servo system driven by AC permanent magnet synchronous motor under different working conditions.Fopid controller has better dynamic performance than traditional controller,and can control nonlinear link better.The optimal parameters of the fractional order PID controller of the feed servo system of CNC machine tools were obtained by using the global search ability of ASGSO algorithm.The feed servo system model of CNC machine tool was established.The comparison of the feed servo system was carried out by PSO-FOPID,STA-FOPID and ASGSO-FOPID respectively.The simulation and experiment results show that the proposed ASGSO-FOPID controller has the advantages of fast tracking speed,strong anti-interference ability and high precision.The method can effectively improve the positioning accuracy and machining accuracy of CNC machine tools.