When spatial modulation Fourier transform spectrometer is used to detect the spectrum of remote target, the interferogram and recovered spectrum are influenced by wavefront distortion resulting from atmospheric turbulence disturbance. According to the phase modulation of atmospheric turbulence disturbance on optical field, we build the model of atmospheric turbulence random phase screen and optical field split-step propagation in atmosphere. The interferogram and recovered spectrum affected by atmospheric turbulence disturbance are calculated numerically. The results show that the atmospheric turbulence disturbance causes low-frequency background intensity fluctuation in interferogram, and the concomitant frequency noise appears at the low-frequency region of the recovered spectrum. The relationship between normalized spectrum error and telescope entrance pupil magnification along with atmospheric coherence length is analyzed by statistical experiment method. The results indicate that the statistical mean of normalized spectrum error is linear positive correlated to telescope entrance pupil magnification, and it is nonlinear negative correlated to atmospheric coherence length. According to the statistical result of the normalized spectrum error, in order to realize the effective detection on target spectrum, the telescope entrance pupil magnification can be designed reasonably on the basis of the atmospheric coherence length in outfield environment.