Forecasting traffic flow is significant for intelligent transportation systems (ITS), such as urban road planning, traffic control, traffic planning, and many more. A flow prediction model aims at forecasting the traffic flow of future time slices at certain regions by learning the historical traffic flow data and environmental information. However, due to the complicated traffic network topology and the dynamicity of traffic patterns in the real world, it is difficult to capture the multi-level spatial dependencies (e.g. global and local impacts to the traffic) and temporal dependencies (e.g. long-term and short-term impacts to the traffic). In this paper, we propose a Multi-step Coupled Graph Convolution Neural network (MCGCN) with temporal attention to capture the spatial and temporal dependencies of different levels in a traffic network, simultaneously, to predict traffic flow. First, a Multi-step Coupled Graph Convolution module (MCGC) is designed to learn the representation of a traffic network by coupling learning the relationship matrices, to capture the different levels’ information of a traffic network. Then, the traffic network information extracted by MCGC is fed into a Multi-step Coupled Graph Gated Recurrent Unit (MCGRU) module to realize the fusion of traffic network information and temporal features. Finally, a Multi-step Coupled Graph Attention mechanism (MCGCAtt) is used to extract the temporal information of historical time steps to predict the future traffic flow. The experiments are conducted on the NYCTaxi and NYCBike datasets, and the evaluation results demonstrate that our proposed model performs better than the eight compared methods.