An infrared image mapping spectrometer is a snapshot imaging spectrometer in the infrared band. Up to now, a complete optical model of the infrared image mapping spectrometer that contains all elements of the system has not been reported. We present the development of a complete Zemax sequential mode optical model. An imaging slicer has been modeled by combining compensated offsets and multi-configuration structures for different angles of flat mirror facets. In addition, we have completed optical modeling of the re-image lens array, prism array, collecting lens, relay lens, and telescope. The optical model was optimized and designed to determine the optical parameters of the image mapping spectrometer as follows: 70 mm focal length, (1.8 deg, 0.9 deg) field of view, 1.2 F/#, and 180*90 image resolution. Performance evaluation of the optical model shows that the root mean square spot diagram radius and the modulation transfer function are close to the diffraction limit. In addition, the keystone and smile distortion of the spectrometer are smaller than one pixel size. Following tolerance analysis, all fabricating errors of the components were maintained within achievable limits.