This paper focuses on the design of a dynamic Petri recurrent fuzzy neural network (DPRFNN), and this network structure is applied to the path-tracking control of a nonholonomic mobile robot for verifying its validity. In the DPRFNN, the concept of a Petri net and the recurrent frame of internal-feedback loops are incorporated into a traditional FNN to alleviate the computation burden of parameter learning and to enhance the dynamic mapping of network ability. Moreover, the supervised gradient-descent method is used to develop the online-training algorithm for the DPRFNN control. In order to guarantee the convergence of path-tracking errors, analytical methods based on a discrete-type Lyapunov function are proposed to determine varied learning rates for DPRFNN. In addition, the effectiveness of the proposed DPRFNN control scheme under different moving paths is verified by experimental results, and its superiority is indicated in comparison with FNN, RFNN, Petri FNN, and PRFNN control systems.