Driven by the double-carbon goal and the construction of novel power system, excavating the adjustable potential of demand-side flexible resources becomes an inevitable trend to help maintain the supply and demand balance. However, the adjustable capacity forecasting problem of load aggregators faces great difficulty and low accuracy since there is not enough actual demand response (DR) data accumulated at present. To this end, this paper proposes a forecasting method for load aggregator based on the graph convolution neural(GCN) network. All customers are classified into several groups according to their historical load profile, and then, tailored DR models are built for each group to construct the response sample library. An undirected graph is established, whose nodes are different clusters, edges are the response characteristics correlation among clusters, and node characteristic matrix is the response characteristics of each cluster. Based on GCN, the forecasting problem is transformed into the regression problem of point characteristics on the graph. Through the message transmission process on the graph, the response characteristics of different clusters could be shared, and both the historical data of the targeted node and other nodes are effectively used to improve the prediction accuracy from both spatial and temporal aspects. Taking the mean absolute percentage error(MAPE) index obtained from the example analysis as an example, compared with long short-term memory(LSTM), support vector machine(SVM), and random forest regression(RFR), the forecasting accuracy of GCN model has increased by 1.83%, 2.10% and 2.72% in terms of RMSE.