Accurate long-term origin-destination demand (OD) prediction can help understand traffic flow dynamics, which plays an essential role in urban transportation planning. However, the main challenge originates from the complex and dynamic spatial-temporal correlation of the time-varying traffic information. In response, a graph deep learning model for long-term OD prediction (ST-GDL) is proposed in this paper, which is among the pioneering work that obtains both short-term and long-term OD predictions simultaneously. ST-GDL avoids the conventional multi-step forecasting and thus prevents learning from prediction errors, rendering better long-term forecasts. The proposed method captures time attributes from multiple time scales, namely closeness, periodicity, and trend, to study the features with temporal dynamics. Besides, two gate mechanisms are introduced over the vanilla convolution operation to alleviates the error accumulation issue of typical recurrent forecast in long-term OD prediction. A method based on graph convolution is proposed to capture the dynamic spatial relationship, which projects the transportation network into a graphical time-series. Finally, the long-term OD prediction results are obtained by combining the extracted spatio-temporal features with external features from the meteorological information. Case studies on a practical dataset show that the proposed model is superior to existing methods in long-term OD prediction problems.