We design an uncooled dual-band infrared optical system whose operating wavelengths include 3-5-μm mid-wave infrared and 8-11-μm long-wave infrared wavelengths. The effective focal length of this system is 21 mm, and the F-number is 2.6. The system comprises four lenses fabricated with germanium and chalcogenide glass (Ge₁₀As₄₀Se₅₀), and the fourth surface is a Q-type asphere. The system is optimized to achieve athermal effect. The design result shows excellent image quality in the temperature range of -40-60 ℃; additionally, the modulation transfer function is close to the diffraction limit. We design an optical system with an even asphere and the same initial parameters and structure. By comparing, we find that the Q-type asphere has more advantages in optical system design: its stronger ability to correct aberration and smaller deviation from the best-fit sphere are conducive to improving fabrication accuracy and efficiency.