The conventional interpolation windowed FFT algorithms will have a greater error when the number of the truncation is not enough. For this reason, a new construction method of multiplication window functions is presented to analyze electrical harmonics. Based on three conventional window functions, this paper constructs nine kinds of window functions and verifies an algorithm for harmonic high-precision analysis based on three-spectrum-line interpolation FFT. The performance of new window functions is listed, and the new window function is used for the harmonic analysis algorithm of three interpolation FFT. Simulation experiments show that the algorithms using multiplication windows has higher accuracy than using conventional window functions when the sample number length is about 10 periods and the polynomial is 5 order. In the practical engineering, the constructed window functions can be chosen as required. This work is supported by National Natural Science Foundation of China (No. 50677048).