This paper studiesthe distributed state estimation problem of large-scale grid with sensor failures in spoofing attacks.The topological relations are introduced to describe the relationship between distributed sensor nodes.A Bernoulli random sequence is used to describe the spoofing attacks and its random characteristics.This article based on Lyapunov method proves the mean square stability and the H_∞ stability of this system.Based on the analysis results and LMI,a distributed state estimator which satisfies the H_∞ performance constraint is designed.Finally,the validity of the designed estimator is verified by numerical simulation.