This study proposes a novel multiple model adaptive control (MMAC) algorithm for a class of nonlinear discrete time systems. The controller consists of a linear indirect adaptive controller, a nonlinear indirect adaptive controller based on neural networks, and a switching mechanism. The control input is generated by the switching mechanism, which selects the candidate controller from the two controllers. The assumption of the nonlinear term is relaxed to linear-bounded when a modified adaptive law is introduced. The restraint that the nonlinear term of the plant should be linear with respect to the control input is removed by resorting to the pole-placement control scheme. The proposed control method can address the properties of non-minimum phase and open-loop instability in the linear part of the plant. The proposed MMAC algorithm can guarantee the bounded-input-bounded-output stability of the proposed closed-loop switching system. A simulation example is presented to demonstrate the effectiveness of the proposed method.