The rapid development of large language models has led to the widespread adoption of Retrieval-Augmented Generation (RAG), which integrates external knowledge to alleviate knowledge bottlenecks and mitigate hallucinations. However, the existing RAG paradigm inevitably suffers from the impact of flawed information introduced during the retrieval phrase, thereby diminishing the reliability and correctness of the generated outcomes. In this paper, we propose Credibility-aware Generation (CAG), a universally applicable framework designed to mitigate the impact of flawed information in RAG. At its core, CAG aims to equip models with the ability to discern and process information based on its credibility. To this end, we propose an innovative data transformation framework that generates data based on credibility, thereby effectively endowing models with the capability of CAG. Furthermore, to accurately evaluate the models’ capabilities of CAG, we construct a comprehensive benchmark covering three critical real-world scenarios. Experimental results demonstrate that our model can effectively understand and employ credibility for generation, significantly outperform other models with retrieval augmentation, and exhibit robustness despite the increasing noise in the context.