Image-side telecentric unobscured optical systems have significant application values in the field of space optics. However, off-axis astigmatism increases with an increase of field of view (FOV), relative aperture and image-side telecentricity, so it's very difficult to design image-side telecentric anastigmatic systems with an ultrawide FOV. To solve these issues, this paper proposes an effective method that is based on the coaxial parent mirrors. By calculating the off-axis aberration optical path of the primary mirror (PM), secondary mirror (SM) and tertiary mirror (TM), and introducing even aspheric surface and adding boundary constraints, a prospective system with a focal length of 400 mm, a relative aperture of 1/3, an FOV of 18° × 6°, and a telecentricity of greater than 0.5°is designed. The design results show that the modulation transfer function (MTF) of the system is greater than 0.7 at the Nyquist frequency of 34 lp/mm, which is close to the diffraction limitation. It has a high imaging quality, thereby proving the image-side telecentric off-axis three-mirror anastigmatic (TMA) system to be effective. © 2021 Elsevier GmbH