Abstract: A non-data-aided frequency offset estimation algorithm of Quadrature Amplitude Modulated (QAM) signal is investigated. Considering the applicable constraint with the low-order QAM signals and high calculation complexity of most frequency offset estimation algorithms, a frequency offset estimation algorithm with the weighted phase histogram is proposed. According to the relation between the phase probability density function of zero frequency offset and the weighted phase histogram, and introducing the multistage estimation algorithm, the peak of second-order moment of the histogram is measured, the frequency offset estimation value can be obtained. Further, the algorithm realizes the process of multistage estimation introducing with the Fast Fourier Transform algorithm. As a result, the calculation processing is simplified and the calculation complexity is reduced. Some simulation results show that the proposed algorithm has perfect estimation performance without the additional information including with the signal-to-noise ratio and constellation and pilots while the signal-to-noise ratio is high.