Accurately predicting traffic flow characteristics is crucial for effective urban transportation management. Emergence of artificial intelligence has led to the surge of deep learning methods for short-term traffic forecast. Notably, Graph Convolutional Neural Networks (GCN) have demonstrated remarkable prediction accuracy by incorporating road network topology into deep neural networks. However, many existing GCN-based models are based on the premise that the graph network is static, which may fail to do justice in replicating the situations in the real World. On one hand, real road networks are dynamic and undergo changes such as road maintenance and traffic control, leading to altered network structures over time. On the other hand, relationships between road sections can fluctuate due to factors like traffic accidents, weather conditions, and other events, which can significantly impact traffic patterns and result in inaccurate predictions if a static network and static relationships between nodes are assumed. To address these challenges, we propose the spatiotemporal dual adaptive graph convolutional network (ST-DAGCN) model for spatiotemporal traffic prediction, which utilizes a dual-adaptive adjacency matrix comprising both a static and a dynamic graph structure learning matrix. The dual-adaptive mechanism can adaptively learn the global features and the local dynamic features of the traffic states by updating the correlations of nodes at each prediction step, while the gated recurrent unit (GRU), which is also a component of the model, extracts the temporal dependencies of traffic data. Through a comprehensive comparison analysis on two real-world traffic datasets, our model has achieved the highest prediction accuracy when compared to other advanced models.