This paper deals with the problem concerned with tracking control for a class of single input and single output(SISO) strict-feedback nonlinear time-delay systems with full-state constraints. Firstly, the state observer is designed for estimating the unmeasured states. Then, by employing the Radial basis function neural networks(RBF NNs), the unknown functions are approximated. Meanwhile, a barrier Lyapunov function is utilized to ensure that the output parameters are restricted and the effects of unknown time-delays are eliminated by choosing appropriate Lyapunov–Krasovskii functions in the design procedure. Finally, an output feedback control scheme is constructed and less learning parameters are used in barrier Lyapunov function backstepping design, and thus reduce the computational burden. It is shown that the designed controller can ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded(SGUUB) and the tracking error converges to a small neighborhood of the origin. An example is presented to illustrate the effectiveness of the proposed method.