Conversational recommender systems enable natural language conversations and thus lead to a more engaging and effective recommendation scenario. As the conversations for recommender systems usually contain limited contextual information, many existing conversational recommender systems incorporate external sources to enrich the contextual information. However, how to combine different types of contextual information is still a challenge. In this paper, we propose a multi-type context-aware conversational recommender system, called MCCRS, effectively fusing multi-type contextual information via mixture-of-experts to improve conversational recommender systems. MCCRS incorporates both structured information and unstructured information, including the structured knowledge graph, unstructured conversation history, and unstructured item reviews. It consists of several experts, with each expert specialized in a particular domain (i.e., one specific contextual information). Multiple experts are then coordinated by a ChairBot to generate the final results. Our proposed MCCRS model takes advantage of different contextual information and the specialization of different experts followed by a ChairBot breaks the model bottleneck on a single contextual information. Experimental results demonstrate that our proposed MCCRS method achieves significantly higher performance compared to existing baselines.