Aiming at a class of cooperative control problems for multi-agent systems with hysteresis inputs， an asymptotic control compensation algorithm of neural network finite-time performance based on a dynamic surface was designed. Firstly， Funnel control was combined with a finite-time performance function to ensure that the consensus error could enter a predefined range in finite time. Second， the unfavorable effects of unknown nonlinear functions within the system and unknown external perturbations were eliminated using Radial Basis Function Neural Network （RBFNN） as well as inequality transformations. In addition， by estimating the upper bounds of some unknown variables， the number of adaptive laws required in the design process was greatly reduced. At the same time， a nonlinear filter with hyperbolic tangent function was proposed to avoid the problem of “differential explosion” in the traditional backstepping control， and eliminate the filter error. Finally， a hysteresis pseudo-inverse compensation signal was designed based on the proposed nonlinear filter to effectively compensate the unknown hysteresis without constructing the hysteresis inverse. Using the Lyapunov stability theory， it is verified that all signals within the closed-loop system are bounded and the consensus error converges to zero asymptotically. Simulation examples also show the effectiveness of the proposed algorithm.