Graph-based search for approximate vector similarity is essential in AI applications, such as retrieval-augmented generation. To support large-scale searches, vector search graphs are often stored on storage devices like SSDs. In this paper, we introduce GraphAccel, an in-storage accelerator optimized for efficient graph-based vector similarity search. Our architecture incorporates an optimized page packing mechanism to reduce SSD page accesses per query, alongside a speculative search scheme that maximizes utilization of idle SSD chips and channels. Through these optimizations, GraphAccel achieves notable performance improvements over existing SSD-based graph search solutions, including DiskANN and DiskANN++.