Conservation of the historical artworks involves carefully planning interventions to prolong the material, historical, and design integrity of humanity's-built heritage. Among which, restoration of the destroyed parts of the artworks via inpainting is one of the most critical stages in the restorative conservation.Indeed, one of the significant assets of any art-historical work is its aesthetic aspects. However, usually due to the visual complexity and the diversity of the motifs, the number of patterns that a restorer artist can have in mind when repairing them, are limited. Also, the inpainting process of such artworks might be very slow and prone to errors; a slight error can cause severe mistakes for the aesthetic aspects of the artifact. Therefore, the need to develop an intelligent system to provide an image of the refurbished artifact before to the restoration operation, is undeniable. Motivated by the idea that the computer-vision-based image inpainting process could be an efficient solution for this purpose, in this paper, for the first time, we propose a framework that employs a deep artificial neural network-based approach to inpaint the images of Persian pottery for restoring their damaged parts. The framework can repair irregular structures that usually exist in Persian pottery and inpaints relatively large missing parts. Besides, the restored parts were seamlessly integrated with the rest of the image without the need for any further postprocessing. To evaluate the proposed framework, we have collected 677 images from different Kubachi ware (known as Persian pottery) to study the inpainting results. The provided dataset is available free for the research community. Quantitative and qualitative evaluations of the results show that the proposed framework performs well, where the inpainted parts are visually and semantically plausible, and the details of the predicted colors in the damaged areas are very satisfying.