Photon-counting detector based X-ray spectral computed tomography (CT), realizes the transformation of CT image from gray to color by increasing energy resolution, which increases material identification capability. However, with increasing the number of energy channels, the channel’s noise increases significantly, which decreases the accuracy of material identification. In order to make full use of the sparsity of spectral CT images and the correlation between spectral CT images, a multi constraint narrow-spectral CT iterative reconstruction algorithm is proposed, which can effectively preserve the edges and details of the image while reducing the noise. Furthermore, principal component analysis (PCA) is used to estimate the spectrum information in narrow spectrum CT images, and the mapping relationship between principal component image and color components R, G, B are established. Finally, the color CT image is obtained. This method can effectively identify materials through the color representation of material components and reduce the background noise in the images. The results of simulation and practical experiments show the proposed reconstruction algorithm is effective, and it is feasible to use PCA for the color characterization of material components.