Energy spectrum computed tomography (CT) can use attenuated data of multiple different energy spectra to obtain narrow energy spectrum projection, which can improve the accuracy of the quantitative characterization of components. Based on the unknown X-ray energy spectrum, a blind CT separation algorithm is proposed to obtain the projection of narrow energy spectrum. First, the X-ray multi-energy spectrum forward model with material prior is established, which can provide energy direction for narrow energy spectrum projection. Second, according to the Poisson statistical characteristics of the measured data, the constrained optimization problem about the energy spectrum fitting coefficient vector and the thickness vector is constructed, and the block coordinate descent algorithm is used to solve the problem. The algorithm can be updated alternately between non-negative matrix factorization and Gaussian-Newton algorithm. The simulation and experimental results show that compared with the existing algorithms, the CT images decomposed by the proposed algorithm have fewer hardening artifacts and noises, and each decomposed projection image conforms to the characteristics of narrow energy spectrum projections, which can improve the accuracy of obtaining narrow energy spectrum projection.