A method called coherent hybrid is proposed to monitor the bias offset drift of Mach-Zehnder modulator (MZM) by mixing the unmodulated local oscillation lightwave with the modulated signal from the same light source and measuring the hybrid power ratio of the maximum to the minimum. The sensitivity at ±5% bias offset is improved from 0.02 dB to 0.3 dB compared with the traditional method by measuring the signal average power. Experiments are carried out with the developed feedback and control system based on this scheme to find the impairment factors and explore the proper solutions. The results reveal the feasibility and effectiveness of the method.