For a class of single-input and single-output discrete-time nonlinear systems，a nonlinear adaptive proportional-integral-differential（PID）control method was proposed by using neural networks and multiple models. Such control method was composed of a linear adaptive PID controller，a neural-based nonlinear adaptive PID controller and a switching mechanism. The linear adaptive PID controller was used to guarantee the boundedness of all signals in the closed-loop system，while the neural-based nonlinear adaptive PID controller was employed to improve the performance of the closed-loop system. By introducing a reasonable switching mechanism，the stability of the closed-loop could be guaranteed，while the control performance was improved. Theoretical analysis illustrated that the proposed control method could guarantee the boundedness of all signals in the closed-loop system，while the tracking error would convergent to any given compact set if the structure and parameters of the neural networks were properly chosen. Then the proposed control method was applied to a continuous stirred tank reactor（CSTR）. Simulation result of CSTR demonstrated the effectiveness of the proposed control method. Since the proposed control method was based on the incremental digital PID controller，it had a bright application prospect in industrial process control.