According to the requirements of an airborne imaging spectrometer for the wide angle and large relative-aperture, an optical system for the airborne imaging spectrometer was designed using an off-axis Schwarzschild telescopic system and a double-Schwarzschild spectral imaging system. The imaging spectrometer has specifications by a field of view of 28°, a relative-aperture of 1/2.5, and working waveband from 04 μm to 1 μm. Based on the astigmatism-correction condition of double-Schwarzschild spectral imaging system, the initial parameters were calculated. Then, the ray tracing and optimization design were performed by ZEMAX software. The analysis and evaluation on the design show that 88% of the encircled energy for centric and edge wavelengths is within one pixel;both smile and keystone are less than 5% of the size of one pixel, so it is easy for spectral and radiation calibrations. Moreover, the MTF of imaging spectrometer is more than 0.59 for different wavelengths, which satisfies the requirements of specifications. As the spectrometer has a smaller volume and lower mass, it is suitable for airborne remote sensing.