Multi-party dialogue machine reading comprehension (MRC) brings an unprecedented challenge due to the multiple speakers and the complex discourse linkages among speaker-aware utterances. The majority of current methods only consider the textual aspects of dialogue situations, and pay little attention to crucial speaker-aware cues. This prevents a model from capturing the speaker’s intention and important discourse information for questions in a complex discourse relationship, leading to the model giving wrong answers. In this paper, we construct a dialogue logic graph module by the relational graph convolutional network (R-GCN) to structure the dialogue information, and design a speaker prediction task to enhance the ability to capture discourse logic. Additionally, we construct a key utterance information decoupling module that focuses on the key discourse information flow involve questions, and filters out noise information. Extensive experiments FriendsQA and Molweni show that our approach outperforms competitive baselines and current state-of-the-art models, especially when dealing with more rounds of dialogue and questions involving people, events and time.