GPS spoofing attack (GSA) has been shown to be one of the most imminent threats to almost all cyber-physical systems incorporated with the civilian GPS signal. Specifically, for our current agenda of the modernization of the power grid, this may greatly jeopardize the benefits provided by the pervasively installed phasor measurement units (PMU). In this paper, we consider the case where synchrophasor data from PMUs are compromised due to the presence of a single GSA, and show that it can be corrected by signal processing techniques. In particular, we introduce a statistical model for synchrophasorbased power system state estimation (SE), and then derive the spoofing-matched algorithms for synchrophasor data correction against GPS spoofing attack. Different testing scenarios in IEEE 14-, 30-, 57-, 118-bus systems are simulated to show the proposed algorithms’ performance on GSA detection and state estimation. Numerical results demonstrate that our proposed algorithms can consistently locate and correct the spoofed synchrophasor data with good accuracy as long as the system observability is satisfied. The accuracy of state estimation is significantly improved compared with the traditional weighted least square method and approaches the performance under the Genie-aided method.