Abstract: Imaging spectrometer requires its optical system have high spatial resolution and spectral resolution over wide field of view and waveband range. A design method for unobstructed, off-axis, reflective optical system was proposed. When pupil and field of view were off-axis properly, obstructing between mirrors was avoided based on the three-mirror anastigmatic. According to the parameters, the unobstructed, off-axis three-mirror anastigmatic systems were designed, when the aperture stop was in front of primary mirror, or on the secondary mirror or focal point of third mirror. The optical system has a spectral region from 1.0 m to 2.5 m, focal length of 1 600 mm, relative aperture of f/5, field of view of angle of 6.861.48. Their imaging qualities reach the diffraction limit and meet the requirements of the imaging spectrometers optical system，which has wide field of view and large relative aperture.