Dynamic synchrophasor measurements play an important role in power system dynamic characteristic monitoring. However, when a fault occur, the decaying DC component in the fault current will have a detrimental effect on dynamic synchrophasor measurement. In this regard, this paper proposes a new dynamic synchrophasor measurement algorithm (DSMA). First, the decaying dc component is described as a dynamic cosine component with a small frequency. Next, a fault current signal model containing the dynamic cosine component and the fundamental component is modelled based on the frequency domain sampling theorem. Finally, the DSMA is accordingly proposed. Simulation results show that, when there are decaying the proposed DSMA is more accurate than the Taylor signal model-based algorithm. Also, the computation burden is very low, which makes the proposed DSMA suitable for practical applications.