Multi-hop question answering (MHQA) poses a significant challenge for large language models (LLMs) due to the extensive knowledge demands involved. Knowledge editing, which aims to precisely modify the LLMs to incorporate specific knowledge without negatively impacting other unrelated knowledge, offers a potential solution for addressing MHQA challenges with LLMs. However, current solutions struggle to effectively resolve issues of knowledge conflicts. Most parameter-preserving editing methods are hindered by inaccurate retrieval and overlook secondary editing issues, which can introduce noise into the reasoning process of LLMs. In this paper, we introduce KEDKG, a novel knowledge editing method that leverages a dynamic knowledge graph for MHQA, designed to ensure the reliability of answers. KEDKG involves two primary steps: dynamic knowledge graph construction and knowledge graph augmented generation. Initially, KEDKG autonomously constructs a dynamic knowledge graph to store revised information while resolving potential knowledge conflicts. Subsequently, it employs a fine-grained retrieval strategy coupled with an entity and relation detector to enhance the accuracy of graph retrieval for LLM generation. Experimental results on benchmarks show that KEDKG surpasses previous state-of-the-art models, delivering more accurate and reliable answers in environments with dynamic information.