Focusing on the issue of adaptive neural tracking control for a class of single input and single output unknown non-affine pure feedback nonlinear switching systems, the mean-value theorem was applied to deal with the non-affine problem successively, and the unknown nonlinear nonlinearities were approximated by radial basis function neural network. Next, the Nussbaum gain technique and the first-order filter were employed to solve the unknown control coefficients and the “explosion of complexity” problem. Finally, a state-feedback controller was proposed by using the common Lyapunov function approach, and the stability of the closed-loop system was analyzed. The proposed controller can decrease the number of learning parameters, and avoid parameter jump when the switch occurs, thus reduces the computational burden. The proposed controller can guarantee that all the signals in the closed-loop system are semi-globally, and the tracking error converges to a small neighborhood of the origin. The simulation results verify the feasibility and effectiveness of the approach.