Doppler wind Lidar is an important method for atmospheric wind measurement. The Doppler frequency shift of backscattering spectrum due to the wind is detected from the transmissions of frequency discrimination. High sensitivity and large dynamic range measurement is difficult for atmospheric wind measurement because of the limitationof frequency discriminator characteristic. In this paper, a frequency discriminator constructed with Dual fiber Mach-Zehnder interferometer is proposed. Two fiber Mach-Zehnder interferometers with different atmospheric wind detection dynamic range and sensitivity are designed and used to measure Doppler frequency shift at the same time. The optical path difference of FMZI-2 is 13.7 cm which can realize large dynamic range wind measurement (±100 m·s-1) and the optical path difference of FMZI-1is designed to be 74.8 cm which can realize high sensitivity detection. Moreover, the absolute wind velocity of FMZI-1 channel can be corrected by the measurement result of FMZI-2 channel. Thus the high sensitivity and large dynamic range wind detection can be realized. The sensitivity, SNR and wind error of two channels are simulated and analyzed for different parameters. The results indicate that the system can realize the wind error less than 1 m·s-1 for large dynamic range(±100 m·s-1) wind velocity, which is a beneficial exploration for high sensitivity and large dynamic range Doppler wind lidar.