This paper studies the consensus control problem for a class of nonlinear multi-agent systems under a directed communication graph. Firstly, the performance function is introduced to make the output error satisfy prescribed performance. Then, the full state constraints problem is solved by employing the Barrier Lyapunov function. The Lyapunov-Krasovskii functional and Young's inequality are used to eliminate the effects of state time-delays. The radial basis function neural networks are used to approximate the unknown nonlinear function. Furthermore, an adaptive event-triggered controller is proposed, such that the outputs of all agents can achieve the consensus. According to the Lyapunov stability theory, the closed-loop systems are semi-globally bounded stability. Finally, the validity of the designed control strategy is verified by simulation.