With the rapid development of social networks and decentralized applications, graph data generated by interactive behavior exhibits significant dynamic characteristics. However, the continuous collection and publication of dynamic graph data pose severe privacy leakage risks. In this context, local differential privacy, as a powerful privacy protection technique that avoids reliance on trusted third parties, has been applied to the collection and synthesis of dynamic graph data. However, existing dynamic graph synthesis methods based on local differential privacy do not fully utilize graph structural information, resulting in low-quality synthesized graphs. This paper proposes SGU, a structure-guided method for updating dynamic graphs under differential privacy. SGU divides dynamic graph update into three subtasks: edge insertion, edge deletion, and node insertion. It incorporates graph structure-based edge insertion mechanisms, edge deletion strategies informed by the importance of triangular structures, and node insertion schemes utilizing asymmetric random response. Theoretical analysis shows that SGU satisfies strict \(\epsilon \) -edge local differential privacy. Experimental results on two real-world datasets, Facebook and Enron, demonstrate that SGU outperforms existing methods in terms of global and local clustering coefficients, as well as community detection similarity.