Accurate Traffic Prediction is a challenging task in intelligent transportation due to the spatial-temporal aspects of road networks. The traffic of a road network can be affected by long-distance or long-term dependencies where existing methods fall short in modeling them. In this paper, we introduce a novel framework known as Spatial-Temporal Multi-Granularity Framework (STMGF) to enhance the capture of long-distance and long-term information of the road networks. STMGF makes full use of different granularity information of road networks and models the long-distance and long-term information by gathering information in a hierarchical interactive way. Further, it leverages the inherent periodicity in traffic sequences to refine prediction results by matching with recent traffic data. We conduct experiments on two real-world datasets, and the results demonstrate that STMGF outperforms all baseline models and achieves state-of-the-art performance.