Time-varying power frequency will cause a non-synchronous sampling phenomenon at a fixed sampling rate and will reduce harmonic detection accuracy. Class A harmonic measuring instruments overcome this problem through hardware phase locking, but their high price makes it difficult for them to be widely used in actual engineering. Achieving accurate harmonic detection by correcting non-synchronous sampling results through reasonable algorithms on the embedded system can reduce equipment costs effectively. First, spectral leakage suppression conditions and multipoint transformation harmonic measurement algorithm characteristics are analyzed, and the influence of different transformation points on the spectrum is studied, and the optimal conversion point selection formula for different sampling conditions is derived. Second, an average reference power frequency optimization algorithm is proposed by prioritizing the calculation of fundamental and low odd harmonic frequency to further improve the overall calculation effect. Finally, the algorithm is implemented on the STM32 embedded system. The simulation data calculation and the experimental results of LED lamp harmonic detection verify the high precision and reliability of the harmonic measurement in the embedded system based on this algorithm in non-synchronous sampling.