Since traffic data has dynamic spatial and temporal dependence features. So timely and accurate traffic forecasting, especially in the medium and long term, remains a challenging problem. For medium and long time prediction, this paper proposes a multi-time granularity spatial-temporal sparse attention model (MGSTSA). The model utilizes the periodic characteristics of traffic data and introduces new spatial-temporal blocks to learn the dynamic spatial and temporal dependence of traffic data at different time granularities. Specifically, the spatial block models local spatial relationships and global spatial relationships for long-distance road segments with similar traffic patterns via GCN and multi-headed sparse self-attention. The temporal block models long-time dependencies using temporal sparse attention networks. Dynamic spatial-temporal dependencies under different features are extracted by combining multiple temporal granularities. The proposed method is evaluated on Xi'an and Jinan traffic speed datasets. Comparing with the better performing GWNET in the baselines, the proposed model reduces the mean absolute error by 16.1 % and 11.3% on the two datasets, for 2 hours forecasting.