During the transmission of power measurement data through communication networks from remote terminal unit (RTU) to the state estimator in Supervisory Control and Data Acquisition (SCADA), power cyber-physical systems (PCPSs) are more susceptible to cyber-attacks. To mitigate that threat, this paper is concerned with a new data recovery strategy on machine learning against false data injection attacks (FDIAs) in PCPSs. Firstly, in view of the limited resources (such as limited energy) of adversaries and system protections, a sparse target false data injection attack (FDIA) is constructed. Then, the FDIA detection problem is transformed into a tripartite separation problem, and the alternating direction method of multipliers on proximal exchange (ADMM-PE) is adopted to complete the intrusion detection of FDIAs. In addition, with the help of reliable mask information and real incomplete measurement data provided by the FDIA detection, a similar supervised generative adversarial imputation networks (GAIN) is proposed to complete the measurement data recovery after FDIAs. Specifically, the pseudo labels generated by data analysis methods such as k-means clustering and support vector machine (SVM) to improve the accuracy of measurement data recovery. Finally, the experimental results of PCPSs show the effectiveness and superiority of the proposed data recovery strategy against FDIAs.