Graph neural networks (GNNs) emerged recently as a powerful tool for analyzing non-Euclidean data such as social network data. Despite their success, the design of graph neural networks requires heavy manual work and domain knowledge. In this paper, we present a graph neural architecture search method (GraphNAS) that enables automatic design of the best graph neural architecture based on reinforcement learning. Specifically, GraphNAS uses a recurrent network to generate variable-length strings that describe the architectures of graph neural networks, and trains the recurrent network with policy gradient to maximize the expected accuracy of the generated architectures on a validation data set. Furthermore, to improve the search efficiency of GraphNAS on big networks, GraphNAS restricts the search space from an entire architecture space to a sequential concatenation of the best search results built on each single architecture layer. Experiments on real-world datasets demonstrate that GraphNAS can design a novel network architecture that rivals the best human-invented architecture in terms of validation set accuracy. Moreover, in a transfer learning task we observe that graph neural architectures designed by GraphNAS, when transferred to new datasets, still gain improvement in terms of prediction accuracy.