Large Language Models (LLMs) and Retrieval-Augmented Generation (RAG) have demonstrated significant potential in automated fact-checking. However, existing methods face limitations in insufficient evidence utilization and lack of explicit verification criteria. Specifically, these approaches aggregate evidence for collective reasoning without independently analyzing each piece, hindering their ability to leverage the available information thoroughly. Additionally, they rely on simple prompts or few-shot learning for verification, which makes truthfulness judgments less reliable, especially for complex claims. To address these limitations, we propose a novel method to enhance evidence utilization and introduce explicit verification criteria, named EVICheck. Our approach independently reasons each evidence piece and synthesizes the results to enable more thorough exploration and enhance interpretability. Additionally, by incorporating fine-grained truthfulness criteria, we make the model's verification process more structured and reliable, especially when handling complex claims. Experimental results on the public RAWFC dataset demonstrate that EVICheck achieves state-of-the-art performance across all evaluation metrics. Our method demonstrates strong potential in fake news verification, significantly improving the accuracy.