The principles and configuration of the high-throughput computed-tomography imaging spectrometer are introduced. Three kinds of dispersers (including direct-view prism) are designed and an iterative reconstruction algorithm is described. Some simulated experiments are made, and the spectral image consisting of 61×61 spatial pixels and 13 spectral bands are obtained. The simulation results show that the theorem is correct, and that the reconstruction algorithm is efficient, convergent and reliable.