Large language models accumulate extensive parametric knowledge through pre-training. However, knowledge conflicts occur when outdated or incorrect parametric knowledge conflicts with external knowledge in the context. Existing methods address knowledge conflicts through contrastive decoding, but in conflict-free scenarios, static approaches disrupt output distribution. Other dynamic decoding methods attempt to measure the degree of conflict but still struggle with complex real-world situations. In this paper, we propose a two-stage decoding method called Dynamic Cognitive Reconciliation Decoding (DCRD), to predict and mitigate context-memory conflicts. DCRD first analyzes the attention map to assess context fidelity and predict potential conflicts. Based on this prediction, the input is directed to one of two decoding paths: (1) greedy decoding, or (2) context fidelity-based dynamic decoding. This design enables DCRD to handle conflicts efficiently while maintaining high accuracy and decoding efficiency in conflict-free cases. Additionally, to simulate scenarios with frequent knowledge updates, we constructed ConflictKG, a knowledge conflict QA benchmark. Experiments on four LLMs across six QA datasets show that DCRD outperforms all baselines, achieving state-of-the-art performance.