The spaceborne dispersive spectrometer is widely used in environmental, resource, and ocean observations. The coded spectrometer has higher energy advantages than the dispersion spectrometer, so it has great application prospects. In the current study, we developed an off-axis short-wave infrared coded optical system (SICOS) based on curved prism dispersion, and we further explored the design and optimization of the SICOS structure. Finite element analyses of a space-based short-wave infrared coded spectrometer based on curved prism dispersion (SSICS-CPD), including static simulation, modal analysis, sinusoidal vibration mechanical analysis, and random vibration mechanical analysis, were carried out. Simulation results showed that the SICOS support structure had excellent mechanical and thermal stability. As off-axis optical systems cannot meet the requirements of optical position accuracy through centering processing, a point source microscope and three-coordinate measuring machines were employed to complete the high-precision and rapid assembly of the SSICS-CPD. In addition, verification tests of surface shape error, stress relief, random vibration, and optical design parameters were carried out to validate the high stability and imaging performance of the SSICS-CPD. Results showed that the average modulation transfer function in the full field was 0.43 at 16.67 lp/mm, the spectral smile was <0.2 pixels, and the spectral keystone was <0.1 pixels. The design, analysis, assembly, and verification of the SSICS-CPD provide a useful reference for the development of other spaceborne prism dispersion spectrometers.