In this article, the problem of tracking control for a class of nonlinear time-varying full state constrained systems is investigated. By constructing the time-varying asymmetric barrier Lyapunov function (BLF) and combining it with the backstepping algorithm, the intelligent controller and adaptive law are developed. Neural networks (NNs) are utilized to approximate the uncertain function. It is well known that in the past research of nonlinear systems with state constraints, the state constraint boundary is either a constant or a time-varying function. In this article, the constraint boundaries both related to state and time are investigated, which makes the design of control algorithm more complex and difficult. Furthermore, by employing the Lyapunov stability analysis, it is proven that all signals in the closed-loop system are bounded and the time-varying full state constraints are not violated. In the end, the effectiveness of the control algorithm is verified by numerical simulation.