A low comlexity frequency offset estimation algorithm based on amplitude ratio is proposed due to the frequency offset between transmitter laser and local oscillator (LO) laser in coherent optical M- ary quadrature amplitude modulation (M-QAM) systems. The proposed algorithm utilizes the relationship between the maximum amplitude and the second largest amplitude of the signal spectrum to estimate the frequency offset accurately, which reduces the computational complexity greatly. A coherent optical 20-Gbaud 16-QAM transmission system with single polarization is simulated to investigate the performance of the proposed estimator with respect to gradient descent(GD) and chirp Z- transform(CZT).The simulation results show that the performance of proposed algorithm does not fluctuate with the distribution of signal frequency and can achieve the very close performance to CZT and GD with three iterations. However, the computational complexity is reduced by over 75% in comparision with algorithms based on CZT and GD with three iterations.