This article addresses the adaptive tracking control problem for switched uncertain nonlinear systems with state constraints via the multiple Lyapunov function approach. The system functions are considered unknown and approximated by radial basis function neural networks (RBFNNs). For the state constraint problem, the barrier Lyapunov functions (BLFs) are chosen to ensure the satisfaction of the constrained properties. Moreover, a state-dependent switching law is designed, which does not require stability for individual subsystems. Then, using the backstepping technique, an adaptive NN controller is constructed such that all signals in the resulting system are bounded, the system output can track the reference signal to a compact set, and the constraint conditions for states are not violated under the designed state-dependent switching signal. Finally, simulation results show the effectiveness of the proposed method.