Relying on the diverse graph convolution operations that have emerged in recent years, graph neural networks (GNNs) are shown to be powerful to deal with high-dimensional non-Euclidean domains, such as social networks or citation networks. Despite the tremendous human efforts been taken to explore new graph convolution operations, there are a few attempts to automatically search operations in GNNs. The search space of GNNs is significantly larger than that of CNNs, because of diverse components in the message-passing of GNNs. This, therefore, prevents the straightforward application of classical NAS methods for GNNs. In this work, we propose a novel dynamic one-shot search space for multi-branch neural architectures of GNNs. The dynamic search space maintains a subset of the large search space along with a set of importance weights for operation candidates in the subset as the architecture parameters. After each iteration, the subset is pruned by removing candidates with low importance weights and is expanded with new operations. The dynamic subsets of operation candidates are not uniform but is individual for each edge in the computation graph of the neural architecture, which can ensure the diversity of operations in the final architecture is as competitive as direct search in the large search space. Our experiments of semi-supervised and supervised node classification on citation networks, including Cora, Citeseer, and Pubmed, demonstrate that our method outperforms the current state-of-the-art manually designed architectures and reaches competitive performance to existing GNN NAS approaches with up to 10 times of speedup.