The technology of interferometric imaging spectrometer can detect spatial information and spectral information of targets simultaneously. It has been the research hotpot because of its advantages of high throughput, high spectral resolution, high spatial resolution and so on. In order to obtain the spectral images of scene at different distance, a system of interferometric imaging spectrometer is presented, which consists of two imaging lens, a collimating lens, a Sagnac transverse shearing splitter and a detector. Based on the analysis of the optical paths and structure of spectrometer, system parameters of interferometric imaging spectrometer were researched, especially the ones of the transverse shearing splitter, incident plane width, mirror offset, optical parallelism error, and the clear aperture of the imaging lens and collimating lens . Optimal system parameters were given by discussing the relationship of parameters including transverse shearing splitter, detection distance, imaging lens, collimating lens and detector. Experimental prototype is set up to verify the impact of the error of system parameters on the imaging properties.