Massive mobile phone data provide continuous and large-scale dynamic origin–destination (OD) flow information for multiple modes of transportation. In this study, we represent the dynamic OD flows obtained from mobile phone data as time-dependent graphs and propose two novel spatial-temporal graph convolutional network (STGCN)-based models to predict dynamic OD flows. Both models directly operate on the graph-structured OD flows, capture correlations among OD flows far apart in the Euclidean space, and fully explore the complex spatial-temporal features. We first formulate OD flows as explicit edges that specify the travels between two locations and propose an edge-focused STGCN. The edge-focused STGCN applies a novel three-step strategy to effectively update edge features in large-scale graphs. Second, we formulate OD flows as vertices in graph and propose a vertex-focused STGCN. The vertex-focused STGCN infers the relations among OD flows by establishing an adjacency matrix based on the temporal similarity between OD flows. The proposed models were validated using real-world mobile phone data collected in Kunshan, China. OD flows in the next hour were predicted, and the mean absolute percent errors of the edge-focused STGCN and the vertex-focused STGCN were 1.755% and 1.672%, respectively; both were significantly lower than the current baseline models.