For a class of constrained nonlinear system with large operating regions and fast time-varying processes, a set of linear parameter-varying(LPV) models are designed as the approximate description of the original nonlinear system. For each LPV model, a local offline predictive controller with the stable region is designed according to the parameter dependent Lyapunov function. Then the overlapped stable regions cover the desired operating regions through the switching strategy in the set of local offline predictive controllers, and the stability of the scheduled controller is guaranteed. Simulation results show that, compared with the well-known scheduled predictive control algorithms, the proposed control strategy not only guarantees the control constraints, but also obtains good control performance with less switching times.