The rapid development of conversational assistants accelerates the study on conversational question answering (QA). However, the existing conversational QA systems usually answer users’ questions with a single knowledge source, e.g., paragraphs or a knowledge graph, but overlook the important visual cues, let alone multiple knowledge sources of different modalities. In this paper, we hence define a novel research task, i.e., multimodal conversational question answering (MMCoQA), aiming to answer users’ questions with multimodal knowledge sources via multi-turn conversations. This new task brings a series of research challenges, including but not limited to priority, consistency, and complementarity of multimodal knowledge. To facilitate the data-driven approaches in this area, we construct the first multimodal conversational QA dataset, named MMConvQA. Questions are fully annotated with not only natural language answers but also the corresponding evidence and valuable decontextualized self-contained questions. Meanwhile, we introduce an end-to-end baseline model, which divides this complex research task into question understanding, multi-modal evidence retrieval, and answer extraction. Moreover, we report a set of benchmarking results, and the results indicate that there is ample room for improvement.