An adaptive hybrid control system using a recurrent neural network (RNN) is proposed to control a permanent magnet linear synchronous motor (PMLSM) servo-drive system. First, a field-oriented mechanism is applied to formulate the dynamic equation of the PMLSM servo-drive. Then, a hybrid control system is proposed to control the mover of the PMLSM servo-drive for periodic motion. In the hybrid control system, the RNN controller is the main tracking controller, which is used to mimic an optimal control law, and the compensated controller is proposed to compensate the difference between the optimal control law and the RNN controller. Moreover, an on-line parameter training methodology of the RNN, which is derived using the Lyapunov stability theorem and the backpropagation method, is proposed to guarantee the asymptotic stability of the control system. In addition, to relax the requirement for the bounds of minimum approximation error and Taylor high-order terms, an adaptive hybrid control system is investigated to control the PMLSM servo-drive, where two simple adaptive algorithms are utilised to estimate the mentioned bounds. The effectiveness of the proposed control schemes is verified by both the simulated and experimental results.