Ship course tracking (i.e., ship heading tracking) system is one of the key systems for maritime navigation. Due to the non-linearity of the ship motion and environmental disturbances, it is relatively challenging to realize the effective control of the ship heading. Moreover, compared with continuous-time systems, discrete-time systems are preferable in practical applications. In this paper, on the basis of continuous ZN (Zhang neurodynamics) PD (proportional and derivative) and PID (proportional, integral and derivative) controllers, discrete ZN-PD and ZN-PID controllers for the ship course tracking are further designed and simulated. Specifically, the Eulerian discretization method is used, which uses numerical differentiation to approximate the derivatives to discretize the continuous controllers into discrete controllers. Finally, the simulation results confirm that both controllers provide effective heading tracking, with the ZN-PD controller exhibiting faster response and the ZN-PID controller effectively improving response speed and providing better tracking for complicated dynamic inputs.