A complete solution for parallel accelerated reconstruction of dual-energy computed tomography (CT) based on graphics processing unit (GPU) is proposed. By integrating the view angle registration steps of dual-energy sampling data into the basic reconstruction process of dual-energy CT, the accuracy of dual-energy projection decomposition is granted, and the accuracy of dual-energy CT reconstruction is improved. Several images are back-projected simultaneously in the back-projection step to avoid repeated calculation of projection addresses, and GPU parallel algorithm is used in each step in the whole reconstruction process to improve the reconstruction speed of dual-energy CT. When the reconstructed images are two and four types, compared with the reconstruction speed of repeated reconstruction by single-energy CT, the speedup ratio of the reconstruction process of the proposed method is 1.88 and 3.24, respectively, and the speedup ratio of the most time-consuming back-projection step is 1.90 and 3.66, respectively. Experiments and practical application prove that the proposed method can effectively improve the accuracy and speed of dual-energy CT reconstruction.