In this paper, a robust adaptive $H{infty}$ control scheme is presented for a class of switched uncertain nonlinear systems. Radical basis function neural networks (RBF NNs) are employed to approximate unknown nonlinear functions and uncertain terms. A robust $H{infty}$ controller is designed to enhance robustness due to the existence of the compound disturbance which consists of approximation errors of the neural networks and external disturbance. Adaptive neural updated laws and switching signals are deducted from multiple Lyapunov function approach. It is proved that with the proposed control scheme, the resulting closed-loop switched system is robustly stable and uniformly ultimately bounded (UUB) such that good capabilities of tracking performance is attained and $H{infty}$ tracking error performance index is achieved. A practical example shows the effectiveness of the proposed control scheme.