Cyber-threats are becoming a big concern due to the potential severe consequences of such threats is false data injection (FDI) attacks where the measures data is manipulated such that the detection is unfeasible using traditional approaches. This work focuses on detecting FDIs for phasor measurement units where compromising one unit is sufficient for launching such attacks. In the proposed approach, moving averages and correlation are used along with machine learning algorithms to detect such attacks. The proposed approach is tested and validated using the IEEE 14-bus and the IEEE 30-bus test systems. The proposed performance was sufficient for detecting the location and attack instances under different scenarios and circumstances.