Graph processing on GPUs received much attention in the industry and the academia recently, as the hardware accelerator offers attractive potential for performance boost. However, the high-bandwidth device memory on GPUs has limited capacity that constrains the size of the graph to be loaded on chip. In this paper, we introduce GPU-based graph traversal on compressed graphs, so as to enable the processing of graphs having a larger size than the device memory. Designed towards GPU’s SIMT architecture, we propose two novel parallel scheduling strategies Two-Phase Traversal and Task-Stealing to handle thread divergence and workload imbalance issues when decoding the compressed graph. We further optimize our solution against power-law graphs by proposing Warp-centric Decoding and Residual Segmentation to facilitate parallelism on processing skewed out-degree distribution. Extensive experiments show that with 2x-18x compression rate, our proposed GPU-based graph traversal on compressed graphs (GCGT) achieves competitive efficiency compared with the state-of-the-art graph traversal approaches on non-compressed graphs.