To the information fusion estimation in distributed multi-sensor network, a consensus algorithm that can improve the convergence speed is proposed.Firstly, the graph theory, the conventional average consensus algorithm and the weighting matrices are introduced.Then, the cost function is defined by the LMS principle and the estimation error between the local node and its neighbor nodes, and the weighting matrices are updated by the cost function.Thus the fast consensus algorithm can be obtained.The parameter selection is also introduced briefly.Simulation was carried out using several common weighting matrices.The results show that the fast consensus algorithm can improve the convergence speed, especially for the sensor network with low connectivity.