Traffic flow prediction has garnered increasing attention in the field of Intelligent Transportation Systems (ITS). Therefore, accurate prediction models are essential for enabling traffic management authorities to guide vehicles more efficiently through the road network. Existing works have employed innovative methods to tackle the traffic prediction problem efficaciously, but the modeling of spatial-temporal correlations in traffic networks and flow data has shown limited effectiveness. Consequently, there is a significant discrepancy between the predicted outcomes and real-world scenarios. In this paper, we introduces a novel deep learning model called the Spatial-Temporal Exponential Smoothing Hybrid Transformer Network (STESHTN) for addressing the traffic flow prediction problem. STESHTN effectively captures both temporal and spatial dependencies. In the temporal dimension, we employ temporal exponential smoothing attention and multi-head self-attention to exploit the temporal associations present in traffic time-series data. In the spatial dimension, we utilize multiple graphs to construct the traffic road network. Our model's superior performance is demonstrated through experiments conducted on four real-world datasets, PEMS03, PEMS04, PEMS07, and PEMS08.