Due to spectrum leakage, traditional harmonic measurement methods based on FFT lead to a larger error in the measurement of the fundamental frequency offset signal or the unsteady periodic signal. Now this paper uses a method of time domain interpolation to reposition asynchronous sampling sequence, segments sequence and analyze it respectively by using linear interpolation algorithm or Hermite interpolation algorithm according to the sequence of second difference quotient. Then two situations that the fundamental frequency offset is fixed and fundamental frequency is fluctuating are calculated. The results show that piecewise interpolation synchronization algorithm can be applied to the above two cases. Taking computational efficiency into account, it can meet the accuracy requirement of GBT 17626.7 -2008 at the same time. The piecewise interpolation synchronization algorithm is a kind of practical method.