Due to the picket fence effect and the problem of spectrum leakage in the case of asynchronous sampling, the measurement accuracy of power harmonic analysis based on fast Fourier transform （FFT）needs to be further improved. Windowing and interpolation algorithms are effective methods to improve the measurement accuracy of FFT harmonic parameters. Based on the sidelobe characteristics of the placing-zeros cosine window and polynomial interpolation algorithms, the power harmonic analysis method of the placing-zeros cosine window FFT is proposed in this paper. Different cosine window functions are designed according to the characteristics of harmonics. Due to the flexibility of window function design, the interpolation algorithm for a certain window function is no longer applicable, so more general bispectral and trispectral interpolation are given. The revised formula provides a new method for FFT-based harmonic analysis. The sidelobe characteristics and the measurent results of the frequency, amplitude and phase of each harmonic are simulated and analyzed. The comparison with the classic Hanning window, Nuttal window, and Rife-Vincent window verifies that the algorithm has higher analysis accuracy of harmonics parameter.