A new design method for unobsured catadioptric infrared optical systems was presented to avoid the obstruction of traditional catadioptric systems. The linear aberration reasons of conventional off-axis two-mirror telescopes were analyzed. As the unobscured optical system is difficult to be designed because of the linear astigmatism in the off-axis two-mirror telescope, the conditions to eliminate the linear astigmatism were discussed. On the conditions, an design idea of unobsured catadioptric optical systems was proposed through associating with coaxal lenses. By combining different relay lenses, two unobsured catadioptric infrared optical systems were implemented for 3-5 μm MW IR and 8-12 μm LW IR applications. The optical design parameters of the two systems are effective focal length of 200 mm, F=2, and the full field of view of 2.75°×2.2°. The performance of the two systems approaches to diffractive limit from Modulation Transfer Function(MTF) curves of all field of view. The design results show that the high performance unobscured catadioptric infrared optical systems will be obtained by combination of zero linear astigmatism confocal off-axis two-mirror telescopes with coaxal lenses.