To solve the problem of cold shield matching in a cooled infrared (IR) imaging optical system with aperture stop placed away from the lens, a pupil matching method based on the telecentric optical structure is proposed. The formulae of Gaussian parameters between the relay lens and the objective lens are derived by using the ideal imaging process. A specific discussion and numerical analysis are carried out. The objective lens is designed as image-space telecentric and the relay lens is designed as object-space telecentric to achieve the requirement that the aperture stop far away from the objective lens. And a specific designing example is added to show the effectiveness of the analysis.