Due to its advantageous imaging characteristic and banding flexibility, imaging fiber bundle can be used for line-plane-switching push-broom infrared imaging. How to precisely couple the fiber bundle in the optics system is the key to get excellent image for transmission. After introducing the basic system composition and structural characteristics of the infrared systems coupled with imaging fiber bundle, this article analysis the coupling efficiency and the design requirements of its relay lenses with the angle of the numerical aperture selecting in the system and cold stop matching of the refrigerant infrared detector. For an actual need, one relay coupling system has been designed with the magnification is -0.6, field of objective height is 4mm, objective numerical aperture is 0.15, which has excellent image quality and enough coupling efficiency. In the end, the push broom imaging experiment is carried out. The results show that the design meets the requirements of light energy efficiency and image quality. This design has a certain reference value for the design of the infrared fiber optical system.