Modeling the spatiotemporal relationship (STR) of traffic data is important yet challenging for existing graph networks. These methods usually capture features separately in temporal and spatial dimensions or represent the spatiotemporal data by adopting multiple local spatial-temporal graphs. The first kind of method mentioned above is difficult to capture potential temporal-spatial relationships, while the other is limited for long-term feature extraction due to its local receptive field. To handle these issues, the Synchronous Spatio-Temporal grAph Transformer (S2TAT) network is proposed for efficiently modeling the traffic data. The contributions of our method include the following: 1) the nonlocal STR can be synchronously modeled by our integrated attention mechanism and graph convolution in the proposed S2TAT block; 2) the timewise graph convolution and multihead mechanism designed can handle the heterogeneity of data; and 3) we introduce a novel attention-based strategy in the output module, being able to capture more valuable historical information to overcome the shortcoming of conventional average aggregation. Extensive experiments are conducted on PeMS datasets that demonstrate the efficacy of the S2TAT by achieving a top-one accuracy but less computational cost by comparing with the state of the art.