In this article, for a class of discrete time non-affine nonlinear systems, a multiple-model-based indirect self-tuning control method is developed. The indirect self-tuning control method is composed of a linear robust indirect self-tuning controller, a nonlinear neural network indirect self-tuning controller and a switching mechanism. By introducing a modified Clarke index, the indirect self-tuning control method can tolerate properties of non-minimum phase and open-loop instability of the controlled system and attenuate the disturbance caused by the higher order nonlinear term. By resorting to the time-varying operation, it is proved without the assumption on the boundedness of the nonlinear term or its differential term that the proposed multiple-model-based nonlinear indirect self-tuning control method can guarantee the bounded-input-bounded-output stability of the closed-loop system and improve the system performance simultaneously. To illustrate the effectiveness of the proposed method, simulations for a synthetic nonlinear system and a realistic nonlinear system are conducted.