Abstract: There have been some research works on the signal time delay (STD) problem in path tracking control, but most of these works are aimed at a specific control method. Among the path tracking control methods, nonlinear model predictive control (NMPC) has the advantage of dealing with the system's constraints explicitly, realizing multi-objective optimization easily, and effectively utilizing the reference path information in front of the controlled object, etc. However, the research on the STD problem in the path tracking control system based on NMPC is relatively immature, which restricts the practical application of this control method. The following research has been carried out to address the above issues. First, a path tracking control system for car-like robots that can better isolate the influence of STD is constructed. Next, the mechanism of STD on the NMPC path tracking control system is analyzed, i.e., the STD causes the position of the car-like robot to be used for generating the control signals by the controller to not correspond to the position of the car-like robot at the time of execution of those control signals. Then, an STD influence abatement method based on growing the NMPC prediction horizon is proposed, i.e., with the iteration period unchanged, the number of the better prediction steps of the STD-free system is added by an integer number above the ratio of the STD and period by a factor of two. Finally, the effectiveness of the proposed method is verified by computer simulation and experiment. The simulation and experiment results show that the STD affects the NMPC path tracking control system, and the NMPC control algorithm that does not consider STD can achieve highly accurate path tracking in STD-free systems, whereas control failure in STD systems. The influence of the STD can be effectively reduced by increasing the prediction horizon. The NMPC controller based on this method can ensure that the displacement error amplitude of the path tracking control is not more than 0.1002m and the heading error amplitude is not more than 0.0291rad in the simulation and experiment systems where the STD is not smaller than 0.2s.