An algorithm of image spectral data cube reconstruction for the computed-tomography imaging interferometer (CTII) is presented. Computed-tomography imaging interferometer combines advantages of both conventional spatially modulated Fourier transformation imaging spectrometer (FTIS) and computed-tomography imaging spectrometer (CTIS) such as high through put, high spectral resolution and high spatial resolution. The working principle of computed-tomography imaging interferometer and the characteristics of the images acquired form computed-tomography imaging interferometer are analyzed, and the method of data cube reconstruction is given. The convolution back-projection (CBP) is used in computed-tomography (CT) reconstruction, which is suitable for multiangular projection. The steps of image reconstruction and corresponding mathematical expression are introduced in detail. The simulations are carried out under the illumination of D65, a target of 396×396 pixels is projected at the range of 0～180°, and the projection interval is 0.5°. Part of the reconstructed images is displayed. The experimental results prove that the method is feasible.