Containing stepped micro- mirror and flaky beam splitter, prefixing objective of spatio- temporally modulated Fourier transform imaging spectrometer is not only to match with parameters of ladder micromirror,but also to have telecentric characteristic with a real entrance pupil. To this end, this paper studies a method to transform the ordinary infrared lens into a telecentric construction with a real entrance pupil.Meanwhile, the study of off axis aberrations caused by the sheet beam splitter and compensation plate proposes a correction method applying a combination of cylindrical and Zernike surface to improve image quality. Based on the method, with the specific requirements of 3~5 mm spectral range, F number of 4, 400 mm effective focal length, no vignetting within full field of view of 4.58° , an infrared optical system is designed.Simulation results show that: the image quality of front objective is closed to the diffraction limit with the maximum root mean square (RMS) spot diameter 5.9 mm in full field, and the distortion less than 0.3% . So this method can be used for the design of the front lens with large aperture in spatio-temporally modulated Fourier transform imaging spectrometer.