This paper focuses on the problem of multi-area interconnected power system secure state estimation under false data injection(FDI) attack. A distributed intermediate observer method is proposed to estimate the system states, FDI attack signals and load deviation of the system simultaneously. Firstly, the states of a power system and the FDI attack are augmented to obtain the equivalent state space model. Then, a distributed intermediate observer is constructed for each power subsystem to fulfill secure estimation, and a compensation control strategy is designed to reduce the impact of FDI attack and load deviation. Finally, the simulation results show that the proposed method is feasible and effective.