This paper presents a novel imaging spectrometer, the Computed-Tomography Imaging Interferometer (CTII). CTII is the combination of the conventional Fourier Transformation Imaging Spectrometer (FTIS) and the Computed-Tomography Imaging Spectrometer (CTIS).This system consists of a telescope system, a collimating system, a Dove prism, a cylindrical lens, a Michelson interferometer, and a focal plane array sensor. Therefore, CTII retains the advantages of both FTIS and CTIS such as high etendue, high spectral resolution and the snapshot ability. In this paper, the basic principle of CTII is introduced. And the experimental system of a CTII is constructed. The experimental results show CTII is feasible.