Influenced by deep penetration of the new generation of information technology, power systems have gradually evolved into highly coupled cyber-physical systems (CPS). Among many possible power CPS network attacks, a false data injection attacks (FDIAs) is the most serious. Taking account of the fact that the existing knowledge-driven detection process for FDIAs has been in a passive detection state for a long time and ignores the advantages of data-driven active capture of features, an active and passive hybrid detection method for power CPS FDIAs with improved adaptive Kalman filter (AKF) and convolutional neural networks (CNN) is proposed in this paper. First, we analyze the shortcomings of the traditional AKF algorithm in terms of filtering divergence and calculation speed. The state estimation algorithm based on non-negative positive-definite adaptive Kalman filter (NDAKF) is improved, and a passive detection method of FDIAs is constructed, with similarity Euclidean distance detection and residual detection at its core. Then, combined with the advantages of gate recurrent unit (GRU) and CNN in terms of temporal memory and feature-expression ability, an active detection method of FDIAs based on a GRU-CNN hybrid neural network is proposed. Finally, the results of joint knowledge-driven and data-driven parallel detection are used to define a mixed fixed-calculation formula, and an active and passive hybrid detection method of FDIAs is established, considering the characteristic constraints of the parallel mode. A simulation system example of power CPS FDIAs verifies the effectiveness and accuracy of the method proposed in this paper.