Graph neural networks (GNNs) have achieved remarkable success in structured prediction, owing to the GNNs’ powerful ability in learning expressive graph representations. However, most of these works learn graph representations based on a static graph constructed by an existing parser, suffering from two drawbacks: (1) the static graph might be error-prone, and the errors introduced in the static graph cannot be corrected and might accumulate in later stages, and (2) the graph construction stage and graph representation learning stage are disjoined, which negatively affects the model’s running speed. In this paper, we propose a joint-learning-based dynamic graph learning framework and apply it to two typical structured prediction tasks: syntactic dependency parsing, which aims to predict a labeled tree, and semantic dependency parsing, which aims to predict a labeled graph, for jointly learning the graph structure and graph representations. Experiments are conducted on four datasets: the Universal Dependencies 2.2, the Chinese Treebank 5.1, the English Penn Treebank 3.0 in 13 languages for syntactic dependency parsing, and the SemEval-2015 Task 18 dataset in three languages for semantic dependency parsing. The experimental results show that our best-performing model achieves a new state-of-the-art performance on most language sets of syntactic dependency and semantic dependency parsing. In addition, our model also has an advantage in running speed over the static graph-based learning model. The outstanding performance demonstrates the effectiveness of the proposed framework in structured prediction.