An imaging spectrometer (IS) can get continuous spectrum and acquire the image of the observed object, and it is used widely in the fields of remote sensing, industrial inspecting, etc. A compact imaging spectrometer system based on computed-tomography principle by using a special designed binary phase grating is described in this paper. The computed tomography imaging spectrometer (CTIS) records the projection data of different direction at the same time. The data cube of the object is acquired by reconstruction of the projection data. The instrument can record both spectral and spatial information of a dynamic scene. As only a 2-D binary phase grating is used as splitter and disperser, there are no moving parts, the system of CTIS becomes very compact. As the key component, the characteristics of grating are important to system stability and accuracy of reconstruction. In our work, the grating is designed and fabricated, and the whole system is set up. The configuration of the system is presented and the method of the spectral and spatial calibration is introduced. The mapping matrix of system is established by the results of calibration. The real object such as a colorful doll or a cluster of flower is imaged by the CTIS. The data cube of the real object is reconstructed by the EM algorithm. The size of the image of the object is about 200*200pixel, and the spectral range is from 410nm to 700nm. The spectral resolution is 10nm which depends on the step of spectral calibration. The accuracy of reconstruction and SNR is analyzed. The experimental results are presented, and the work is proven to be encouraging.