Hyperspectral X-ray CT (HXCT) technology provides not only structural imaging but also the information of material components therein. The main purpose of this study is to investigate the effect of various reconstruction algorithms on reconstructed X-ray absorption spectra (XAS) of components shown in the CT image by means of HXCT. In this paper, taking 3D printing polymer as an example, seven kinds of commonly used polymers such as thermoplastic elastomer (TPE), carbon fiber reinforced polyamide (PA-CF), acrylonitrile butadiene styrene (ABS), polylactic acid (PLA), ultraviolet photosensitive resin (UV9400), polyethylene terephthalate glycol (PETG), and polyvinyl alcohol (PVA) were selected as samples for hyperspectral CT reconstruction experiments. Seven kinds of 3D printing polymer and two interfering samples were divided into a training set and test sets. First, structural images of specimens were reconstructed by Filtered Back-Projection (FBP), Algebra Reconstruction Technique (ART) and Maximum-Likelihood Expectation-Maximization (ML-EM). Secondly, reconstructed XAS were extracted from the pixels of region of interest (ROI) compartmentalized in the images. Thirdly, the results of principal component analysis (PCA) demonstrated that the first four principal components contain the main features of reconstructed XAS, so we adopted Artificial Neural Network (ANN) trained by the reconstructed XAS expressed by the first four principal components in the training set to identify that the XAS of corresponding polymers exist in both of test sets from the training set. The result of ANN displays that FBP has the best performance of classification, whose ten-fold cross-validation accuracy reached 99%. It suggests that hyperspectral CT reconstruction is a promising way of getting image features and material features at the same time, which can be used in medical imaging and nondestructive testing.