Traditional recommender systems estimate user preference on items purely based on historical interaction records, thus failing to capture fine-grained yet dynamic user interests and letting users receive recommendation only passively. Recent conversational recommender systems (CRSs) tackle those limitations by enabling recommender systems to interact with the user to obtain her/his current preference through a sequence of clarifying questions. Despite the progress achieved in CRSs, existing solutions are far from satisfaction in the following two aspects: 1) current CRSs usually require each user to answer a quantity of clarifying questions before reaching the final recommendation, which harms the user experience; 2) there is a semantic gap between the learned representations of explicitly mentioned attributes and items. To address these drawbacks, we introduce the knowledge graph (KG) as the auxiliary information for comprehending and reasoning a user's preference, and propose a new CRS framework, namely Knowledge Enhanced Conversational Reasoning (KECR) system. As a user can reflect her/his preference via both attribute- and item-level expressions, KECR closes the semantic gap between two levels by embedding the structured knowledge in the KG. Meanwhile, KECR utilizes the connectivity within the KG to conduct explicit reasoning of the user demand, making the model less dependent on the user's feedback to clarifying questions. KECR can find a prominent reasoning chain to make the recommendation explainable and more rationale, as well as smoothen the conversation process, leading to better user experience and conversational recommendation accuracy. Extensive experiments on two real-world datasets demonstrate our approach's superiority over state-of-the-art baselines in both automatic evaluations and human judgments.