Fourier transform spectrometers are widely used in the field of infrared spectroscopy. They are also the remote sensing instruments suitable for profiling atmospheric temperature, humidity and wind field and atmospheric composition. A Fourier transform spectrometer based on a Mach-Zehnder interferometer is proposed. A set of reflectors in the Mach-Zehnder interferometer move at a uniform linear velocity to vary the Optical Path Difference (OPD) between double arms linearly. Then, a balanced photo-receiver detects the interference signals from double paths differentially. Through the Fourier transform of the electric signals corresponding to linear optical path difference, the spectral distribution curve of input light can be obtained. Compared with the Michelson interferometer, the interference signals obtained by the Mach-Zehnder interferometer under the same optical flux input condition is stronger and the noise due to non coherence intensity is less. This result is of significance to the space remote sensing.