Traffic prediction is a classical spatial-temporal prediction problem with many real-world applications such as intelligent route planning, dynamic traffic management, and smart location-based applications. Due to the high nonlinearity and complexity of traffic data, deep learning approaches have attracted much interest in recent years. However, few methods are satisfied with both long and short-term prediction tasks. Target at the shortcomings of existing studies, in this paper, we propose a novel deep learning framework called Long Short-term Graph Convolutional Networks (LSGCN) to tackle both traffic prediction tasks. In our framework, we propose a new graph attention network called cosAtt, and integrate both cosAtt and graph convolution networks (GCN) into a spatial gated block. By the spatial gated block and gated linear units convolution (GLU), LSGCN can efficiently capture complex spatial-temporal features and obtain stable prediction results. Experiments with three real-world traffic datasets verify the effectiveness of LSGCN.