Dual-energy computed tomography (DECT) has been widely used to medical imaging, security inspection, nondestructive testing, materials science and so on, with its capability to decompose and identify materials and provide quantified results. DECT technique can accurately decompose two basis materials due to its performance to acquire the attenuation information of the scanned object at low and high energies. However, when there are three basis materials, if the direct inverse material decomposition (DIMD) is used to decompose the materials, the material CT images will contain much noise and artifacts. Therefore, we propose an image domain multi-material decomposition algorithm for DECT based on dictionary learning (DL) and relative total variation(RTV), which is called DL-RTV for short. The method employs the DIMD to acquire original material images, and then trains a dictionary to explore the sparsity of the images and improve the accuracy of the material decomposition. Meanwhile, the RTV is introduced to further reduce the noise and artifacts of the images and preserve details. In addition, the constrains of mass conservation and the bounds of each pixel are added into the DL-RTV model to enhance the material decomposition accuracy. Simulation and experimental results indicate that the DL-RTV method can decompose three kinds of materials accurately, suppress the noise and artifact of the basis images and improve the material discrimination. The method is authenticated to be effective and practical, which has important significance for the development and application of DECT.