In the case of non-synchronous sampling and non-integer periodic truncation, the use of Fast Fourier Transform (FFT) for power harmonic analysis is likely to cause spectrum leakage and the fence effect. Windowed interpolation can effectively solve the problem. The spectral characteristics of the Nuttall window are analyzed and the 4 terms 5 orders Nuttall window is deduced. The Nuttall self-convolution window function is obtained by a self-convolution operation based on the 4 terms 5 orders Nuttall window, and the four-spectral-line interpolation correction formula is derived. Based on the phase stability of all-phase FFT (apFFT), the ratio of the amplitude of the main spectrum line and the side spectrum line near the theoretical frequency point, a spectrum correction analysis method based on the interpolation of Nuttall double windows and apFFT double spectrum line is deduced. A new combination algorithm of windowed interpolation FFT for frequency and amplitude detection and apFFT for phase detection is proposed. The simulation results show that the new combined algorithm proposed in this paper has higher accuracy and stronger ability to suppress spectrum leakage in harmonic detection. This work is supported by National Natural Science Foundation of China (No. 51667020).