Various correlations hidden in crowdsourcing annotation tasks bring opportunities to further improve the accuracy of label aggregation. However, these relationships are usually extremely difficult to be modeled. Most existing methods can merely make use of one or two correlations. In this paper, we propose a novel graph neural network model, namely LAGNN, which models five different correlations in crowdsourced annotation tasks by utilizing deep graph neural networks with convolution operations and derives a high label aggregation performance. Utilizing the group of high quality workers through labeling similarity, LAGNN can efficiently revise the preference among workers. Moreover, by injecting a little ground truth in its training stage, the label aggregation performance of LAGNN can be further significantly improved. We evaluate LAGNN on a large number of simulated datasets generated through varying six degrees of freedom and on eight real-world crowdsourcing datasets in both supervised and unsupervised (agnostic) modes. Experiments on data leakage is also contained. Experimental results consistently show that the proposed LAGNN significantly outperforms six state-of-the-art models in terms of label aggregation accuracy.