Because the non-synchronous sampling and non-integral period truncation can result the spectrum leakage and fence effect, the window functions and interpolation algorithms has been used in the fast Fourier transform (FFT) to improve the precision of harmonics analysis. This paper has introduced the construction method of mutual-multiplication window function. And we have verified an algorithm for harmonic analysis based on three-spectrum-line interpolation FFT. Three kinds of window function were given various weights to construct new window function. Then the new window functions have been applied to the harmonics analysis method based on three-spectrum-line interpolation FFT. The simulation experiments show that constructs the mutual function relative to the conventional window function interpolation algorithm has a higher accuracy. In the practical engineering we can choose them according the performance of constructed window function.