Flight delay prediction has recently gained growing popularity due to the significant role it plays in efficient airline and airport operation. Most of the previous prediction works consider the single-airport scenario, which overlooks the timevarying spatial interactions hidden in airport networks. In this paper, the flight delay prediction problem is investigated from a network perspective (i.e., multi-airport scenario). To model the time-evolving and periodic graph-structured information in the airport network, a flight delay prediction approach based on the graph convolutional neural network (GCN) is developed in this paper. More specifically, regarding that GCN cannot take both delay time-series and time-evolving graph structures as inputs, a temporal convolutional block based on the Markov property is employed to mine the time-varying patterns of flight delays through a sequence of graph snapshots. Moreover, considering that unknown occasional air routes under emergency may result in incomplete graph-structured inputs for GCN, an adaptive graph convolutional block is embedded into the proposed method to expose spatial interactions hidden in airport networks. Through extensive experiments, it has been shown that the proposed approach outperforms benchmark methods with a satisfying accuracy improvement at the cost of acceptable execution time. The obtained results reveal that deep learning approach based on graph-structured inputs have great potentials in the flight delay prediction problem.