Spectral leakage in Fourier transform will influence the accuracy of harmonic analysis for asynchronous sampling. The commonly used windowed interpolated FFT algorithm (WIFFTA) can improve the measurement accuracy by windowing the time samples and interpolating the DFT coefficients, but the accuracy is restricted by the frequency resolution. A new algorithm for harmonic analysis is proposed in this paper, which tries to adjust the actual sample sequence to an ideal sampling sequence synchronous with the original signal on the basis of the time-domain Newton's interpolation algorithm. Simulation results show this algorithm can increase the accuracy of harmonic analysis by reducing spectral leakage efficiently despite the variation of frequency resolution. In addition, it can improve the computation efficiency and it is suitable to analyze the fluctuating signals.