Slot filling and intent detection are two major tasks for spoken language understanding. In most existing work, these two tasks are built as joint models with multi-task learning with no consideration of prior linguistic knowledge. In this paper, we propose a novel joint model that applies a graph convolutional network over dependency trees to integrate the syntactic structure for learning slot filling and intent detection jointly. Experimental results show that our proposed model achieves state-of-the-art performance on two public benchmark datasets and outperforms existing work. At last, we apply the BERT model to further improve the performance on both slot filling and intent detection.