In order to meet the demand that unobscured three-mirror optical systems should be small volume with excellent optical performance,a circular three-mirror optical system was proposed.A coaxial three-mirror system is calculated by the paraxial matrix as a starting point.With the condition that the focal point of each conic mirror is placed to coincide successively,elements in the system are tilted and decentered properly to make the system unobscured and to fold the optical path in the region surrounded by three mirrors to reduce the system volume.Zernike polynomial surfaces which are symmetric about tangential plane are used to correct aberrations and to improve the image quality.An uncooled long wave infrared optical system is designed at focal length 310mm,F-number 1.55 with field of view 1.774°×1.331°.The modulation transfer function of this system is above 0.52 all over the field of view at the Nyquist frequency of 20 line pairs per millimeter.