This paper focuses on the problem of multi-area interconnected power system security state estimation under false data injection (FDI) attack. A distributed intermediate observer design method is proposed to estimate the system state, FDI attack signals and load deviation of the system simultaneously. In particular, the design of the intermediate observer does not need to satisfy the strictly positive real condition of the system or the observer matching condition. Firstly, the states of power system and the FDI attack are augmented to obtain the equivalent state space model. Then, a distributed intermediate observer is constructed for secure estimation, and a compensation control strategy is designed to reduce the impact of FDI attack and load deviation on the safe operation of power system. Finally, the simulation results show that the proposed method is feasible and effective.