Phasor measurement units (PMUs) are taking an increasingly important role in power system dynamic security monitoring and control. However, traditional discrete Fourier transforms (DFTs) used by PMUs cannot obtain accurate phasor measurements during frequency excursion and transient events, being limited by its static phasor model. In this paper, a synchrophasor estimation algorithm for M-class PMUs based on the dynamic phasor model is proposed. In this algorithm, the dynamic phasor within an observation data window is approximated by the second-order Taylor expansion. The linear relationship between the second-order coefficients of the Taylor expansion and the errors caused by the DFT averaging effect is explored. Then, the linear relationship is used to compensate the raw measurement errors under a dynamic condition. Two digital filters are applied not only to eliminate the spectrum leakage caused by the dynamic inputs, but also to make the PMU immune to the out-of-band signals. The algorithm is investigated through simulation, laboratory experiments, and real data from the power system according to IEEE C37.118.1. The test results demonstrate that the proposed algorithm can meet the requirements of the standards.