In this work, we propose a novel high-precision frequency estimation method based on harmonic expansion technique and a simple FFT-based algorithm. By increasing the information content through harmonic expansion in spectral domain instead of sampling time length in time domain, the proposed method can greatly improve the frequency estimation precision, needless to introduce other complex algorithms. The harmonic expansion process is to synthetize multiple harmonic components of the fundamental frequency of the input signal, which are detected to perform high-precision frequency estimation. The proposed method is analyzed in theory and numerical analysis, and demonstrated in experiment. The harmonic expansion in the experiment is achieved by microwave photonics technology through optical comb generation by electro-optical modulation. The signal optical comb containing wideband optical harmonic components are downconverted into low frequency band in electrical domain through optical harmonic sampling. Through digital signal processing on the 2th ~ 12th harmonic components with the FFT-based algorithm, the frequency estimation precision of a single RF tone is improved by about dozens of times as compared with the measurement value of the 1th fundamental frequency. This method is also compatible with other existing FFT-based high-precision frequency estimation algorithms and has the potential for a variety of application scenarios, such as Radar/LIDAR, spectrum sensing, vibration measurement and electronic reconnaissance.