Aiming at the monitoring requirements of wide-area detection and human activity carbon emission sources, this paper proposes a design scheme for a wide-area high-resolution greenhouse gas imaging spectrometer for multi-gas collaborative detection. By combining the vector aberration theory with free-form surface optimization design, a large field of view and high-resolution system is achieved. Moreover, in response to the problems of an excessively large system size and the susceptibility to interference in spatial layout when both a large field of view and high resolution are considered, a multi-component coated prism color separation technology is proposed. An orthogonal combined color separation prism system is designed as a relay system. After optimization, the overall spatial layout is in the shape of a "windmill", with a compact structure. Finally, the optical system design of the spectrometer with large relative aperture, large swath width, and multiple channels is realized, with a field of view angle of 14° and a spatial resolution of 0.5 km. The imaging quality of each channel's optical system is close to the diffraction limit at the Nyquist frequency. This research provides a feasible solution for the wide-area high-precision detection of spaceborne greenhouse gas imaging spectrometers and the accurate calculation of human carbon emission sources.