Dependency parses are an effective way to inject linguistic knowledge into many downstream tasks, and many practitioners wish to efficiently parse sentences at scale. Recent advances in GPU hardware have enabled neural networks to achieve significant gains over the previous best models, these models still fail to leverage GPUs' capability for massive parallelism due to their requirement of sequential processing of the sentence. In response, we propose Dilated Iterated Graph Convolutional Neural Networks (DIG-CNNs) for graphbased dependency parsing, a graph convolutional architecture that allows for efficient end-to-end GPU parsing. In experiments on the English Penn TreeBank benchmark, we show that DIG-CNNs perform on par with some of the best neural network parsers.