The introduction of information and communication technologies makes network environments increasingly open, leaving smart-grid control systems incredibly vulnerable to malicious attacks. False data injection (FDI) attacks stealthily tamper with measurement data, resulting in erroneous decisions made by the control center that greatly influence the normal operation of the power system. By taking advantage of real-time data acquisition with edge computing, in this article, we propose a scheme based on classification of predicted residuals (CPRs) for the FDI attack detection. The CPR scheme first predicts the acquired measurement data at the edge of the sensing network via developing an accurate prediction model. Followed the novel real-time classification method under the edge devices supporting, it classifies the predicted residuals independent of the false data to enhance the detection accuracy. Through these two steps, the detection rate of FDI attacks is greatly improved. The proposed scheme is validated in a real microgrid testbed. Experimental results show that the CPR scheme performs well in detecting FDI attacks and remains sensitive in injection attack probability and magnitude. The detection scheme even has effectiveness at low injection attack probability and magnitude (5% and 0.018 per thousand, respectively). Furthermore, it also proves that the proposed scheme has applicability in high real-time requirements at the edge of smart grids.