This paper proposed a neural network model algorithm control (NNMAC) method for the path tracking control of differentially steered wheeled mobile robots (WMRs) subject to nonholonomic constraints. The model algorithm control (MAC) is a one-step-ahead predictive controller, in which the control law is obtained by minimizing the output error. The MAC method needs the well known model of the controlled system to design the controller. But sometimes it is difficult to get the accurate model of the controlled system or the model of the controlled system is not good because of the inside and outside disturbances and unknown parameters. Neural network has the ability to estimate the nonlinear system’s model and its corresponding inverse model. In this paper the NNMAC method which combines two neural networks and MAC method is proposed to do the path tracking control of a wheeled mobile robot. Some simulations are conducted to show the performance and feasibility of the proposed control strategy. In these simulations the WMR is controlled to track two difference reference paths such as the circular shape path and the “8” shape path.