With the aid of large language models, current conversational recommender system (CRS) has gaining strong abilities to persuade users to accept recommended items. While these CRSs are highly persuasive, they can mislead users by incorporating incredible information in their explanations, ultimately damaging the long-term trust between users and the CRS. To address this, we propose a simple yet effective method, called PC-CRS, to enhance the credibility of CRS's explanations during persuasion. It guides the explanation generation through our proposed credibility-aware persuasive strategies and then gradually refines explanations via post-hoc self-reflection. Experimental results demonstrate the efficacy of PC-CRS in promoting persuasive and credible explanations. Further analysis reveals the reason behind current methods producing incredible explanations and the potential of credible explanations to improve recommendation accuracy.
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