In this article, an adaptive neural network (NN) tracking control scheme is proposed for uncertain multi-input-multi-output (MIMO) nonlinear system in strict-feedback form subject to system uncertainties, time-varying state constraints, and bounded disturbances. The radial basis function NNs (RBFNNs) are adopted to approximate the system uncertainties. By constructing the intermediate variables, the external disturbances that cannot be directly measured are approximated by the disturbance observers. The time-varying barrier Lyapunov function (TVBLF) is constructed to guarantee the boundedness of the errors lie in the sets. To overcome the potential singularity problem that the denominator of the barrier function term approaches zero in controller design, the adaptive NN tracking control scheme with time-varying state constraints is proposed. Based on the TVBLF, the controller will be designed to guarantee tracking performance without violating the appropriate error constraints. The analysis of TVBLF shows that all closed-loop signals remain semiglobally uniformly ultimately bounded (SGUUB). The simulation results are performed to validate the validity of the proposed scheme.