A recurrent fuzzy neural network (RFNN) using genetic algorithm (GA) is proposed to control the mover of a linear induction motor (LIM) servo drive for periodic motion in this paper. First, the dynamic model of an indirect field-oriented LIM servo drive is derived. Then, an on-line training RFNN with backpropagation algorithm is introduced as the tracking controller. Moreover, to guarantee the global convergence of tracking error, analytical methods based on a discrete-type Lyapunov function are proposed to determine the varied learning rates of the RFNN. In addition, a real-time GA is developed to search the optimal weights between the membership layer and the rule layer of RFNN on-line. The theoretical analyses for the proposed RFNN using GA controller are described in detail. Finally, experimental results show that the proposed controller provides high-performance dynamic characteristics and is robust with regard to plant parameter variations and external load disturbance.