In this paper, a kind of snapshot imaging spectrometer is designed by using image replication based on Wollaston prism. The system includes telephoto lens, collimator lens, Wollaston prism, the imaging lens and compensation filters. With this optical system, we can obtain two-dimensional information at different wavelengths of the same target through one time exposure. When Light beam is passing Wollaston prisms, in order to make sure that the different wavelengths will not overlap, the Wollaston prism needs to be designed with relatively large beam splitting angle. Then the incidence angle of the imaging lens is relatively large. It will increase the difficulty of the imaging lens design. We design, analyze the principle and the characteristics of the snapshot imaging spectrometer using image replication based on Wollaston prism, and design a complete set of imaging spectrometer system. The structure is complex; the aperture of the optical system must be well matched. In order to make sure that we can obtain good image quality through the single lens, but also the whole system, we design the telephoto lens which is imaging telecentric structure, the collimator lens which is objective telecentric structure. We use the multiple structures in ZEMAX to optimize the 16 spectral bands. At 56 lp·mm-1, the MTF is close to the diffraction limit, the RMS of the SPT is in the Airy disk, proving good image quality.