This paper investigates the problem of mean square bipartite consensus for multi-agent systems under false data injection (FDI) attacks. First, considering the cooperative and competitive interaction among the agents, under the framework of the Kalman filter, a novel algorithm for estimating the states of neighboring agents is designed and the stability of the algorithm is theoretically proved. Unlike related work, the proposed algorithm takes into account the correlation of agents within and outside the measurement range of the estimator. The experimental results show that the estimation algorithm has better estimation performance than the local Kalman filter algorithm. Meanwhile, a security protection mechanism based on a state estimation algorithm is addressed, so that the state update of the agent can adopt a safe value, which eliminates the impact of FDI attacks and ensures that the system can achieve mean square bipartite consensus asymptotically. Finally, the theoretical results are verified by several numerical simulations.