Social network contains the interaction between social members, which constitutes the structure and attribute of social network. The interactive relationship of social network contains a lot of personal privacy information. The direct release of social network data will cause the disclosure of privacy information. Aiming at the dynamic characteristics of social network data release, a new dynamic social network data publishing method based on differential privacy was proposed. This method was consistent with differential privacy. It is named DDPA (Dynamic Differential Privacy Algorithm). DDPA algorithm is an improvement of privacy protection algorithm in static social network data publishing. DDPA adds noise which follows Laplace to network edge weights. DDPA identifies the edge weight information that changes as the number of iterations increases, adding the privacy protection budget. Through experiments on real data sets, the results show that the DDPA algorithm satisfies the user’s privacy requirement in social network. DDPA reduces the execution time brought by iterations and reduces the information loss rate of graph structure.