Abstract: The measurement data in the state estimation is vulnerable to malicious tampering by false data injection attacks, which reduces the reliability of the state estimation. Based on the low-dimension characteristics of measurement data and the sparse characteristics of data attacks, this paper proposed a method detecting power system false data attack by using nonconvex matrix decomposition. First, the false data injection attacks detection was regarded as a sparse and low-rank matrix decomposition problem and then transformed into a nonconvex optimization, which was solved by the improved alternating direction multiplier method. The normal measurement matrix and attack matrix were separated from the attacked data matrix. Then, the attack matrix was used to detect the value and location of the false data injection attacks, and the measurement matrix was used to obtain the correct state variables. Finally, the detection results of IEEE14-bus system were analyzed by different attack amplitudes and verified the accurateness of the proposed method.