Compared with the traditional Doppler frequency discriminator Fabry-Perot interferometer, Mach-Zehnder interferometer (MZI) has the advantages in high transmittance, linear parallel fringes instead of circular rings and wide field of view. An incoherent Doppler wind lidar system is demonstrated based on a fringe-imaging MZI. The mathematical model of wind velocity retrieval is derived, and the field widening of MZI is also used to optimize the performance of lidar system. The ideal fringe pattern outputs are obtained by numerical simulation, and the SineSqr function fitting method is proposed to determine the high-precision displacement of fringes after a Doppler shift. Furthermore, the field widening of MZI can be realized by field compensation which reduces the effect of the incidence angle on optical path difference. The results show that the wind velocity error obtained by SineSqr function fitting method is less than 0.45 m·s-1 at the line-of-sight wind velocity in a range from -100 m·s-1 to 100 m·s-1, which overcomes the instability of wind velocity retrieval by the gravity method. A full-angle field of view of 1° for MZI frequency discriminator without significant performance reduction is also achieved. These supplied discussion of the application techniques for Doppler lidar based on MZI fringe technique would promote the practical development of Doppler lidar for wind velocity measurement of the middle and upper atmosphere.