The method error of gravity method and the measurement error due to system shot noise in wind lidar based on Fizeau interferometer are analyzed in detail. The correction technique of the method error is given, the formula of measurement error is derived. The low troposphere signal simulated by Monte-Carlo technique is used to retrieve the wind velocity. The results show that the method error is related to aerosol-molecule backscattering ratio and the measurement error is related to signal intensity and aerosol-molecule backscattering ratio. At altitude of 0 to 5 km, wind velocity error measured by using fringe technique is below 1m/s.