In this paper, we propose ExtraV, a framework for near-storage graph processing. It is based on the novel concept of graph virtualization, which efficiently utilizes a cache-coherent hardware accelerator at the storage side to achieve performance and flexibility at the same time. ExtraV consists of four main components: 1) host processor, 2) main memory, 3) AFU (Accelerator Function Unit) and 4) storage. The AFU, a hardware accelerator, sits between the host processor and storage. Using a coherent interface that allows main memory accesses, it performs graph traversal functions that are common to various algorithms while the program running on the host processor (called the host program) manages the overall execution along with more application-specific tasks. Graph virtualization is a high-level programming model of graph processing that allows designers to focus on algorithm-specific functions. Realized by the accelerator, graph virtualization gives the host programs an illusion that the graph data reside on the main memory in a layout that fits with the memory access behavior of host programs even though the graph data are actually stored in a multi-level, compressed form in storage. We prototyped ExtraV on a Power8 machine with a CAPI-enabled FPGA. Our experiments on a real system prototype offer significant speedup compared to state-of-the-art software only implementations.