As a common network attack method, False data injection attack (FDLA) can often cause serious consequences to the power system due to its strong concealment. Attackers utilize grid topology information to carefully construct covert attack vectors, thus bypassing the traditional bad data detection (BDD) mechanism to maliciously tamper with measurements, which is more destructive and threatening to the power system. To address the difficulty of detecting them effectively, a detection method based on adaptive interpolation-adaptive inhibition extended Kalman filter (AI-AIEKF) is proposed in this paper. By the adaptive interpolation strategy and exponential weight function, the AI-AIEKF algorithm can improve the estimation accuracy and enhance the robustness of the EKF algorithm. Combined with the weight least squares (WVS), the two estimators respond to the system at different speeds, and the consistency test is introduced to detect the FDLAs. The extensive simulations on the IEEE-14-bus demonstrate that FDIAs can be accurately detected, thus validating the validity of the method.