Computed tomography (CT) images are often impaired by unfavorable artifacts caused by metallic implants within patients, which would adversely affect the subsequent clinical diagnosis and treatment. Although the existing deep-learning-based approaches have achieved promising success on metal artifact reduction (MAR) for CT images, most of them treated the task as a general image restoration problem and utilized off-the-shelf network modules for image quality enhancement. Hence, such frameworks always suffer from lack of sufficient model interpretability for the specific task. Besides, the existing MAR techniques largely neglect the intrinsic prior knowledge underlying metal-corrupted CT images which is beneficial for the MAR performance improvement. In this paper, we specifically propose a deep interpretable convolutional dictionary network (DICDNet) for the MAR task. Particularly, we first explore that the metal artifacts always present non-local streaking and star-shape patterns in CT images. Based on such observations, a convolutional dictionary model is deployed to encode the metal artifacts. To solve the model, we propose a novel optimization algorithm based on the proximal gradient technique. With only simple operators, the iterative steps of the proposed algorithm can be easily unfolded into corresponding network modules with specific physical meanings. Comprehensive experiments on synthesized and clinical datasets substantiate the effectiveness of the proposed DICDNet as well as its superior interpretability, compared to current state-of-the-art MAR methods. Code is available at https://github.com/hongwang01/DICDNet.