Graphs provide a powerful means for representing complex interactions between entities. Recently, deep learning approaches are emerging for representing and modeling graph-structured data, although the conventional deep learning methods (such as convolutional neural networks and recurrent neural networks) have mainly focused on grid-structured inputs (image and audio). Leveraged by the capability of representation learning, deep learning based techniques are reporting promising results for graph applications by detecting structural characteristics of graphs in an automated fashion. In this paper, we attempt to advance deep learning for graph-structured data by incorporating another component, transfer learning. By transferring the intrinsic geometric information learned in the source domain, our approach can help us to construct a model for a new but related task in the target domain without collecting new data and without training a new model from scratch. We thoroughly test our approach with large-scale real corpora and confirm the effectiveness of the proposed transfer learning framework for deep learning on graphs. According to our experiments, transfer learning is most effective when the source and target domains bear a high level of structural similarity in their graph representations.