In this paper, we propose the stability condition of receding horizon control for nonlinear discrete-time switched systems. First, we propose the nonlinear inequality condition on the terminal cost. Under this condition, noninceasing monotonicity of the saddle point value of the finite horizon dynamic game are shown to be guaranteed. Then, we show that receding horizon value function is input-to-state stable (ISS) with respect to the external disturbance with this nonlinear inequality condition on the terminal cost for nonlinear discrete-time systems. Using this result, the new stability condition is derived for receding horizon control scheme of nonlinear discrete-time switched systems.