Traffic forecasting is a typical spatio-temporal data forecasting task with complex spatio-temporal dependencies. Recent works use predefined static graphs and adaptive graphs to reflect real-world traffic patterns. However, traffic networks often suffer from unexpected changes, and the graph structures learned during training phases are not always applicable during testing phases. To cope with this issue, we propose a Position-Aware Dynamic Graph Convolutional Recurrent Network (PADGCRN) for traffic forecasting. First, we design a novel position-aware dynamic graph learning method to obtain dynamic spatial representations. Unlike previous methods, our approach generates dynamic graphs based on the spatio-temporal position embeddings, which more effectively capture hidden spatial correlations. Then, by integrating dynamic graph diffusion convolution into gated recurrent unit, our method is able to capture synchronous spatio-temporal dependencies. Experiments on two real traffic speed datasets verify that effectiveness and efficiency of PADGCRN compared to 12 baselines.