The GPS is vulnerable to GPS spoofing attack (GSA), which leads to disorder in time and position results of the GPS receiver. In power grids, phasor measurement units (PMUs) use GPS to build time-tagged measurements, so they are susceptible to this attack. As a result of this attack, sampling time and phase angle of the PMU measurements change. In this paper, a neural network GPS spoofing detection (NNGSD) with employing PMU data from the dynamic power system is presented to detect GSAs. Numerical results in different conditions show the real-time performance of the proposed detection method.