In the case of non-synchronous sampling and in non-integral period truncation, the fast Fourier transform (FFT) can’t analyze harmonic parameters correctly. So the window functions and interpolation algorithms are made to improve the accuracy of harmonic parameter computation by FFT. This paper derives an algorithm based on four-spectrum-line interpolation. This algorithm uses the four most spectrum lines around true location to computer the accuracy position of the harmonic spectrum line through analyzing the discrete-time Fourier transform of the windowed signal. Then the true values of frequency, amplitude and phase can be calculated. Based on four-spectrum-line interpolation algorithm, this paper gives four practical rectification formulas by using the polynomial approximation method. It is proved that the phase difference of any two adjacent spectrum is . According to this rule, this paper induces a rapid algorithm so that square root is only calculated one time when analyzing some harmonic parameters. The algorithm can save computing complexity and computing time greatly. The simulation results show that the four-spectrum-line interpolation algorithm has higher precision than double/triple- spectrum-line interpolation algorithm especially when estimating the even harmonics and the order of polynomial is lower than two others if obtaining same precision.