Spaceborne ocean colour remote sensing urgently requires large relative-aperture and wide field of view imaging spectrometer. Based on the research objective of large relative-aperture and wide field of view, a spaceborne imaging spectrometer optical system is designed using a folded Schmidt telescope and a modified Dyson spectral imaging system. The relative-aperture of which is 1/1.2, the field of view of hyperspectral image is 3.9°, and the working waveband is from 0.35 μm to 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 the analysis of the design results are performed by ZEMAX software. The analyzed results demonstrate that the MTFs for different wavelengths are all about 0.77, both the line bending and the band bending of the spectrum are less than 6% of the pixel, which is easy for spectral and radiometric calibration. The design results satisfy the requirements of specifications with a small volume and suitable for spaceborne remote sensing.