As an indispensable part in Intelligent Traffic System (ITS), the task of traffic forecasting inherently subjects to the following three challenging aspects. First, traffic data are physically associated with road networks, and thus should be formatted as traffic graphs rather than regular grid-like tensors. Second, traffic data render strong spatial dependence, which implies that the nodes in the traffic graphs usually have complex and dynamic relationships between each other. Third, traffic data demonstrate strong temporal dependence, which is crucial for traffic time series modeling. To address these issues, we propose a novel framework named Structure Learning Convolution (SLC) that enables to extend the traditional convolutional neural network (CNN) to graph domains and learn the graph structure for traffic forecasting. Technically, SLC explicitly models the structure information into the convolutional operation. Under this framework, various non-Euclidean CNN methods can be considered as particular instances of our formulation, yielding a flexible mechanism for learning on the graph. Along this technical line, two SLC modules are proposed to capture the global and local structures respectively and they are integrated to construct an end-to-end network for traffic forecasting. Additionally, in this process, Pseudo three Dimensional convolution (P3D) networks are combined with SLC to capture the temporal dependencies in traffic data. Extensively comparative experiments on six real-world datasets demonstrate our proposed approach significantly outperforms the state-of-the-art ones.