Machine reading comprehension models based on deep learning have achieved remarkable success recently. However, these models have significant defects in constructing long-distance and global semantic relationships, which affect their performance in reading comprehension tasks. Moreover, when reasoning over passage text, most of them simply regard it as a word sequence without exploring rich semantic relationships between words. In order to solve this problem, this paper proposes a new system effective graph structure named Dynamic Conversational Graph Network (DCGN). Firstly, named entities are extracted from the text, and the semantic relationship between syntactic structure and sentence is used for modeling. Then, the context-embedded representation based on serialization structure and the entity node embedded representation based on graph structure are fused by semantic fusion module. Finally, dynamic graph neural network is used to realize machine reading comprehension. The model dynamically builds inference graphs of questions and session history during each round of conversation, which can effectively capture the semantic structure information and the history flow of the conversation. Experimental results show that the model performs well on two recent session challenges (CoQA and QuAC).