It is difficult to perform high accurate harmonic detection with traditional signal peak spectral lines interpolation algorithm due to spectrum leakage under the non-synchronous sampling conditions. Aiming at this problem, an improved algorithm based on frequency shift is proposed, and the detection error of the traditional interpolation algorithm is analyzed, an improved rectification formula is deduced. The algorithm is implemented in three steps, firstly, the frequency of interpolation is rectified based on Hanning window function, then, relative frequency deviation is used to calculate quasi-synchronous sequence based on frequency shift. Secondly, the quasi-synchronous sequence is adopted to rectify frequency of interpolation based on Hanning window function again, two of the relative frequency deviations are added together for rectifying frequency, the spectrum leakage can be reduced by the method. Finally, in order to improve the detection accuracy of amplitude and phase, the quasi-synchronous sequence is adopted to calculate them directly based on the Flat-top window function, the inversion formula need not be deduced. Simulation and experimental results verify that improved algorithm has much higher detection accuracy than that of the traditional signal peak spectral lines interpolation algorithm, both of detection accuracy and anti-noise performance are better than four-spectral-line interpolation algorithm and phase difference correction algorithm in the noise environment. The effectiveness and accuracy of the algorithm is verified by the results of the simulation. This work is supported by National Natural Science Foundation of China (No. 51677163).