Multi-party Dialogue Reading Comprehension is a reading comprehension task that involves comprehending dialogue with multiple interlocutors and answering questions. Research on MDRC faces enormous challenges because of the multiple parties involved and the frequent changes in the chat topic. Previous work has explored in mining and modeling dialogue context features on the basis of pre-trained models and graph-based models. However, two issues exist: insufficient connection between the behavioral events of dialogue participants and excessive information irrelevant to the question during reasoning. In this paper, we propose a dual-graph reasoning with integrated key-clue parsing approach. We utilize the dual-graph reasoning strategy to capture the global structure and internal dynamics of the dialogue. Moreover, we design the key-clue parsing module to prioritize essential dialogue content, which significantly reduces the burden on the model and enhances the accuracy of our model. The experiments on the benchmark dataset show that our approach yields stable and substantial improvements, and outperforms the state-of-the-art methods.