Click-through rate (CTR) prediction is an essential task in web applications such as online advertising and recommender systems, whose features are usually in multi-field form. The key of this task is to model feature interactions among different feature fields. Recently proposed deep learning based models follow a general paradigm: raw sparse input multi-filed features are first mapped into dense field embedding vectors, and then simply concatenated together to feed into deep neural networks (DNN) or other specifically designed networks to learn high-order feature interactions. However, the simple \emph{unstructured combination} of feature fields will inevitably limit the capability to model sophisticated interactions among different fields in a sufficiently flexible and explicit fashion. In this work, we propose to represent the multi-field features in a graph structure intuitively, where each node corresponds to a feature field and different fields can interact through edges. The task of modeling feature interactions can be thus converted to modeling node interactions on the corresponding graph. To this end, we design a novel model Feature Interaction Graph Neural Networks (Fi-GNN). Taking advantage of the strong representative power of graphs, our proposed model can not only model sophisticated feature interactions in a flexible and explicit fashion, but also provide good model explanations for CTR prediction. Experimental results on two real-world datasets show its superiority over the state-of-the-arts.