A Fourier transform imaging spectrometer (FTIS) of medium and long wave infrared bispectrum spatiotemporal joint modulation based on static interference system is presented, and the front telephoto system and post-imaging system are designed. According to the theory of aberration, the initial structure of the reflective front telephoto system is calculated by adding the constraint. The large-scale astigmatism and coma aberration caused by the tilt beam splitter and compensation plate in the system are corrected through the optimization of the optical design software. The modulation transfer function (MTF) of the front telephoto system is close to the diffraction limit in the range of the medium wave and long wave bispectrums. The transmission structure is adopted in the two post-imaging systems of the spectrometer. The results of spot diagram show that the root mean square (RMS) values of the imaging spots of the post-imaging systems are less than 7.0 μm in the bispectrum range. The overall optical system is made up of the front telephoto system and the post-imaging system, whose field of view is 1.5°, medium wave channel F number is 4 and long wave channel F number is 2. In bispectrum range, the spot diagram RMS value of the overall system is less than 10.7 μm, and the MTF of the overall system is more than 0.5 at the detector’s characteristic frequency of 17 lp/mm. The overall system has a good imaging effect.