Recently, graph-based hashing that learns similarity-preserving binary codes via an affinity graph has been extensively studied for large-scale image retrieval. However, most graph-based hashing methods resort to intractable binary quadratic programs, making them unscalable to massive data. In this paper, we propose a novel graph convolutional network-based hashing framework, dubbed GCNH, which directly carries out spectral convolution operations on both an image set and an affinity graph built over the set, naturally yielding similarity-preserving binary embedding. GCNH fundamentally differs from conventional graph hashing methods which adopt an affinity graph as the only learning guidance in an objective function to pursue the binary embedding. As the core ingredient of GCNH, we introduce an intuitive asymmetric graph convolutional (AGC) layer to simultaneously convolve the anchor graph, input data, and convolutional filters. By virtue of the AGC layer, GCNH well addresses the issues of scalability and out-of-sample extension when leveraging affinity graphs for hashing. As a use case of our GCNH, we particularly study the semisupervised hashing scenario in this paper. Comprehensive image retrieval evaluations on the CIFAR-10, NUS-WIDE, and ImageNet datasets demonstrate the consistent advantages of GCNH over the state-of-the-art methods given limited labeled data.