Double Amici prism is a kind of composite prism, as the dispersion component of the imaging spectral system, avoiding some problems of the single dispersion prism. We should give out the each angle′s processing targets of the double Amici prism. Every angle error has a different effect on the dispersion. We design a coded aperture imaging spectral system. A double Amici prism is designed to meet the needs of the applications of the specific system. The mathematical model of the double Amici prism dispersion is deduced from the standpoint of ray tracing. In this particular optical system, we give out the effect of every angle of the prism on the line dispersion, then analyze of the angular error chain′s effect on the line dispersion, and finally give out the production index of the prism. The results contribute to the processing and production of the prism.