Based on backstepping, an adaptive neural network control scheme is proposed for a class of perturbed strictfeedback nonlinear systems with unknown time-varying delays and virtual control coefficients. By choosing appropriate Lyapunov-Krasovskii functionals, the unknown time-varying delay uncertainties can be compensated for. The continuous approximation functions are constructed to solve the singularity problem which occurs when neural networks are used to approximate the unknown nonlinear functions. By introducing a new intermediate variable, the derivative of virtual control is guaranteed to be right. Simulation results show that the proposed controller can guarantee that all the signals in the closed-loop system are semi-global uniformly ultimately bounded, and the tracking error converges to a neighborhood of zero.