Airborne ocean colour remote sensing requires wide angle and large relative-aperture hyperspectral imager. Based on the research objective of wide angle and large relative-aperture, an airborne hyperspectral imager optical system is designed using an off-axis Schwarzschild telescope and a modified Dyson spectral imaging system. The field of view of hyperspectral image is 40°, relative-aperture is 1/1.8, and working waveband is 0.35~1.05 μm. Based on the aberration theory, the principle of spherical aberration correcting is analyzed in modified Dyson spectral imaging system. Ray tracing, optimization and analysis are performed by Zemax software. Results show that the modulation transfer functions for all wavelengths are bigger than 0.82; both smile and keystone are less than 5% of the pixel size. It is convinient for spectral and radiation calibration. The designed optical system satisfies the requirements of specifications, and it is small and light, suitable for airborne remote sensing.