For a class of nonlinear multi-agent systems, an adaptive dynamic surface state constrained quantized control scheme with an adjustable finite-time prescribed performance function is investigated. The major properties of the proposed control algorithm are: 1)This method is combined with the barrier Lyapunov function(BLF) to restrict the states of the multi-agent system, thus the constructed constraint function can adjust its own parameters according to the current tracking error of the system without manual intervention. 2)By applying the dynamic surface control method, the “differential explosion” phenomenon of the traditional backstepping control method is avoided, and the filtered compensating function is designed to eliminate the filter error and signal chattering caused by the dynamic surface method. 3)The RBF neural network is utilized to approximate the unknown nonlinearities in the system, and the quantizer is introduced to reduce the communication burden of the system. The presented quantized control strategy requires only that the quantizer has the sector bounded property. The stability analysis demonstrates that all signals of the closed-loop are semi-globally uniformly bounded. Simulation section verifies the effectiveness of the proposed control scheme.