The coded aperture imaging spectrometer system based on the double-Amici-prism is designed in this paper, which includes the telescope objective, the coded template, the double-Amici-prism, the collimator lens and the imaging lens. This optical system can obtain a high diffraction efficiency. Compared to the imaging spectrometer system with a slit for this kind of system, the field of view is a two-dimensional spatial expansion, increasing the difficulty of design. For the subsequent data inversion algorithm, perfect imaging is needed, and based on this, the optical aberration of the system should be corrected carefully wildly. In this paper, we design and analyse the features of the imaging spectrometer system based on the double-Amici-prism, then the comple imaging spectrometer system. Telescope objective is designed to be telecentric, its MTF at 39 line pairs is 0.8, implying that good images can be obtained. Innovatively, an inverted telescope objective is used as a collimation system.The imaging spectrometer system's MTF at 39 line pairs is higher than 0.65. The imaging of the outdoor target scene, obtained by the coded aperture imaging spectrometer, proves that the design principle is feasible,the system is of high diffraction efficiency, the full-field imaging is of good quality, and the full spectrum of data is creditabe.