To meet the commands of Spatial Heterodyne Spectrometer(SHS) based on Fourier Transform that are high spectral resolution, minimum distortion, homogeneous illumination, high signal to noise ratio and the limited resources of volume and weight, an imaging optical system of SHS was designed. According to the characteristic of spatial interference in SHS, the interferogram on the location plane of the fringes near the gratings was imaged onto the detector with a specific magnification, which determined the spectral resolution and the band width of SHS. For the case of SHS in which magnification was the limit factor, the constant magnification could be obtained by use of the match of fore lens and rear lens to achieve a telecentric optical system. The imaging optical system actually contained a spread of optical elements from grating to detector, and hence, the diffracted wavefront error of gratings and RMS change in wavefront error of beam splitter and field widened wedges in interferometer would decrease the modulation efficiency. The imaging optical system offered the constant magnification, and it is apparent that even minor change in the position of FPA have a slight effect on the spectral resolution and band width, furthermore, the maximum distortion decreases to less than 0.1% over the field of view. The theoretical Modulation Transfer Function (MTF) is high than 0.60 at the spatial frequency in cycles per mm of 38.5 over the entire defined format. Based on the analysis of stray light, uniformly illumination and the ability of field widened of interferometer contained in the imaging optical system, a tolerance sensitivity analysis to determine the worst tilted error of the filter is performed. The optical system has well suited to SHS applications that require high spectral resolution and high modulation efficiency over a relative narrow spectral band.