Recent deep learning models have moved beyond low-dimensional regular grids such as image, video, and speech, to high-dimensional graph-structured data, such as social networks, brain connections, and knowledge graphs. This evolution has led to large graph-based irregular and sparse models that go beyond what existing deep learning frameworks are designed for. Further, these models are not easily amenable to efficient, at scale, acceleration on parallel hardwares (e.g. GPUs). We introduce NGra, the first parallel processing framework for graph-based deep neural networks (GNNs). NGra presents a new SAGA-NN model for expressing deep neural networks as vertex programs with each layer in well-defined (Scatter, ApplyEdge, Gather, ApplyVertex) graph operation stages. This model not only allows GNNs to be expressed intuitively, but also facilitates the mapping to an efficient dataflow representation. NGra addresses the scalability challenge transparently through automatic graph partitioning and chunk-based stream processing out of GPU core or over multiple GPUs, which carefully considers data locality, data movement, and overlapping of parallel processing and data movement. NGra further achieves efficiency through highly optimized Scatter/Gather operators on GPUs despite its sparsity. Our evaluation shows that NGra scales to large real graphs that none of the existing frameworks can handle directly, while achieving up to about 4 times speedup even at small scales over the multiple-baseline design on TensorFlow.