An all-fiber incoherent wind lidar system was proposed and designed based on double-edge technique of optical fiber Mach-Zehnder interferometer. The algorithms for Doppler shift extraction and for wind velocity retrieval were theoretically analyzed. The optical fiber Mach-Zehnder interferometer used as a spectral analyzer in the proposed system, was discussed to optimize for wind velocity measurement based on the signals backscattered by the molecules. Performances including wind measurement sensitivity, signal-to-noise ratio and measurement error of lidar system were numerically simulated based on the U.S. standard atmospheric model. For a ground-based molecular wind lidar at a wavelength of 532 nm, an error in the line-of-sight velocity component of the wind was found to be smaller than 1.4 m/s up to an altitude of 20 km, with the line-of-sight wind velocity within the range of ± 100 m/s, a 300-shot average and a vertical resolution of 1 000 m. Obtained results show that the designed system can be applied for long-distance and large-scale wind velocity measurement. The system will be able to provide a technical solution for the development of the compact Doppler lidar.