A fixed-time consensus control method was proposed for full-state constrained Multi-Agent System （MAS） with unknown perturbations in a fixed undirected graph topology. Firstly， a novel Unified Universal Barrier Function （UUBF） was designed to convert the constrained MAS into a unconstrained system. Secondly， based on the unconstrained system， a neural network was used to approximate the unknown nonlinear term in the system， and a fixed-time state observer was constructed to compensate the neural network update rate through the observation error and improve the approximation ability of the neural network. Thirdly， a new fixed-time disturbance observer was designed to accurately estimate composite perturbation consisting of the unknown perturbation and the approximation error. Fourthly， according to the observed values， a fixed-time control law was constructed using backstepping， and a fixed-time differentiator was designed to solve “differential explosion” problem in backstepping design. Finally， the fixed-time consensus stability condition of MAS was derived and obtained by using the fixed-time consensus theory and Lyapunov stability theorem， and the effectiveness of the designed control method was verified by simulation.