This paper investigates the problem of robust stabilization of a class of switched nonlinear system with uncertain dynamics where each subsystem represents a non-minimum phase. The authors first construct a stabilizing sliding mode controller for each subsystem to stabilize individually its own unstable internal dynamics. Then, a switching strategy is introduced to select the most appropriate diffeomorphism through an infinity of diffeomorphisms. Sufficient conditions are specifically given for the exponential stability and the exponential upper bound of the trajectory of the switched subsystem, which guarantees the global asymptotical stability of the resulting switched system. Obviously, the proposed control approach can improvemore the transient state, compared to a feedback linearization based on only one diffeomorphism. Simulation studies illustrate the effectiveness of the suggested approach.