Hybrid pull-push computational model can provide compelling results over either of single one for processing real-world graphs. Programmability and pipeline parallelism of FPGAs make it potential to process different stages of graph iterations. Nevertheless, considering the limited onchip resources and streamline pipeline computation, the efficiency of hybrid model on FPGAs often suffers due to wellknown random access feature of graph processing. In this paper, we present a hybrid graph processing system on FPGAs, which can achieve the best of both worlds. Our approach on FPGAs is unique and novel as follow. First, we propose to use edge block (consisting of edges with the same destination vertex set), which allows to sequentially access edges at block granularity for locality while still preserving the precision. Due to the independence of blocks in the sense that all edges in an inactive block are associated with inactive vertices, this also enables to skip invalid blocks for reducing redundant computation. Second, we consider a large number of vertices and their associated edge-blocks to maintain a predictable execution history. We also present to switch models in advancewith few stalls using their state statistics. Our evaluation on a wide variety of graph algorithms for many realworld graphs shows that our approach achieves up to 3.69×speedup over state-of-the-art FPGA-based graph processing systems.