This paper focuses on the development of a Petri-fuzzy-neural-network (PFNN) control for an indirect field-oriented linear-induction-motor (LIM) drive. First, an indirect field-oriented mechanism for a LIM drive is derived to preserve the decoupling control characteristic. Then, the concept of a Petri net (PN) is incorporated into a traditional FNN (TFNN) to form a new type of PFNN framework for alleviating the computation burden. Moreover, the supervised gradient descent method is used to develop the online training algorithm for the PFNN. In order to guarantee the convergence of tracking error, analytical methods based on a discrete-type Lyapunov function are proposed to determine the varied learning rates of the PFNN. With the proposed PFNN control system, the mover position of the controlled LIM drive possesses the advantages of good transient control performance and robustness to uncertainties for the tracking of periodic reference trajectories. In addition, the effectiveness of the proposed control scheme is verified by both numerical simulations and experimental results. Furthermore, the superiority of the proposed PFNN control system is indicated in comparison with the TFNN control system