With the widespread popularization of social network platforms, user-generated content and other social network data are growing rapidly. It is difficult for social users to select interested contents from the numerous social data. To alleviate information overload problem and enhance overall user experience of social networks, recommendation systems relying on historical behavioural data and social friendship relations of users, are widely used in social networks. Although researches on social recommendations have been conducted in recent years, recommendation systems of social networks still suffer from several challenges, such as data sparsity and lower performance. Since graph neural network has huge advantages in graph data learning by aggregating neighbors representations of the central node, it has been gathering pace in recent years. In this survey, we review graph neural network based literature for solving recommendation problems in social networks. We first introduce backgrounds of graph neural network and recommendation systems in social networks. Then, for different types of recommendation problems in social networks, we review different graph neural network based recommendation methods briefly. In particular, we first review GNN-based methods for general social recommendation and then review GNN-based methods for different social recommendation scenarios (such as friend recommendation and point-of-interest recommendation). Finally, we briefly discuss promising future directions of the graph neural network based recommendation in social networks.