This paper addresses a neural adaptive backstepping control with dynamic surface control technique for a class of semistrict feedback nonlinear systems with bounded external disturbances. Neural networks(NNs) are introduced as approximators for uncertain nonlinearities and the dynamic surface control(DSC) technique is involved to solve the so-called "explosion of terms" problem. In addition, the NN is used to approximate the transformed unknown functions but not the original nonlinear functions to overcome the possible singularity problem. The stability of closed-loop system is proven by using Lyapunov function method, and adaptation laws of NN weights are derived from the stability analysis.Finally, a numeric simulation validates the results of theoretical analysis.