Abstract: The detection problem of covert false data injection attack (FDIA) for smart grids by using adaptive Kalman filter (AKF) is herein presented. The state-space model of the smart grid is employed to study the characteristics of the random attack and the FDIA. However, an accurate analysis revealed that the commonly used χ²-detector could only detect random attack efficiently, but not the FDIA. To overcome this drawback, the AKF is applied to assess FDIA by analyzing the covert characteristics of the FDIA and the change of actual noise. Finally, the simulation experiments verify the effectiveness of the proposed FDIA detection method.