Collaborative filtering recommendation systems are facing the data sparsity problem associated with interaction data, and social recommendations introduce user social information to alleviate this problem. Existing social recommendation methods cannot express the user interaction interest and social influence deeply, which limits the recommendation performance of the system. To address this problem, in this paper we propose a graph neural network social recommendation algorithm integrating multi-head attention mechanism. First, based on the user-item interaction graph and social network graph, the graph neural network is used to learn the high-order relationship between users and items and deeply extract the latent features of users and items. In the process of learning user embedding vector representation based on the social network graph, the multi-head attention mechanism is introduced to increase the importance of friends with high influence. Then, we make rating predictions for the target users according to the learned user embedding vector representation and item embedding vector. The experimental results on the Epinions dataset show that the proposed method outperforms the existing methods in terms of both Recall and Normalized Discounted Cumulative Gain.