This paper studies the problem of tracking control for a class of constrained nonlinear switched systems with external disturbances. The control objective is to make the state tracking error of the system converge in a finite time and satisfy the given prescribed performance conditions. A hybrid controller including robust stability controller and model predictive controller is designed for each subsystem. Based on the selected Lyapunov functions of the subsystems, a suitable switching law is designed. It is demonstrated that the system can achieve the control objective by using the Lyapunov stability theory. Simulation results verify the effectiveness of the proposed control strategy.