Synchrohasor measurement is a common tool to monitor system stability and detect faults in electric power systems and various Phasor Measurement Units (PMUs) have been developed for this purpose. Parameter computation methods of PMUs specifically designed for rapidly time-varying voltage cases caused by nonlinear dynamic loads have been an attractive research topic. In this paper, instantaneous amplitudes and phases of the voltage signals are estimated using a method based on quadrature amplitude modulation complying with M class accuracy criteria defined by the IEEE Standard C37.118. It has been shown on simulated voltage data that the proposed method provides synchrophasor results satisfying the accuracy limits defined in IEEE Standard C37.118. The results of the proposed method have also been compared with those of the DFT method and the proposed method has been shown to be more advantages in terms of satisfying the accuracy limits and reducing processing time.