Social graphs, representing online friendships among users, are one of the fundamental types of data for many applications, such as recommendation, virality prediction and marketing in social media. However, this data may be unavailable due to the privacy concerns of users, or kept private by social network operators, which makes such applications difficult. Inferring user interests and discovering user connections through their shared multimedia content has attracted more and more attention in recent years. This paper proposes a Gaussian relational topic model for connection discovery using user shared images in social media. The proposed model not only models user interests as latent variables through their shared images, but also considers the connections between users as a result of their shared images. It explicitly relates user shared images to user connections in a hierarchical, systematic and supervisory way and provides an end-to-end solution for the problem. This paper also derives efficient variational inference and learning algorithms for the posterior of the latent variables and model parameters. It is demonstrated through experiments with over 200k images from Flickr that the proposed method significantly outperforms the methods in previous works.