In this article, we pay attention to develop an event-triggered adaptive neural network (ANN) control strategy for stochastic nonlinear systems with state constraints and time-varying delays. The state constraints are disposed by relying on the barrier Lyapunov function. The neural networks are exploited to identify the unknown dynamics. In addition, the Lyapunov-Krasovskii functional is employed to counteract the adverse effect originating from time-varying delays. The backstepping technique is employed to design controller by combining event-triggered mechanism (ETM), which can alleviate data transmission and save communication resource. The constructed ANN control scheme can guarantee the stability of the considered systems, and the predefined constraints are not violated. Simulation results and comparison are given to validate the feasibility of the presented scheme.