The Bulk Synchronous Parallel(BSP) computational model has emerged as the dominant distributed framework to build large-scale iterative graph processing systems. While its implementations(e.g., Pregel, Giraph, and Hama) achieve high scalability, frequent synchronization and communication among the workers can cause substantial parallel inefficiency. To help address this critical concern, this paper introduces the GraphHP(Graph Hybrid Processing) platform which inherits the friendly vertex-centric BSP programming interface and optimizes its synchronization and communication overhead. To achieve the goal, we first propose a hybrid execution model which differentiates between the computations within a graph partition and across the partitions, and decouples the computations within a partition from distributed synchronization and communication. By implementing the computations within a partition by pseudo-superstep iteration in memory, the hybrid execution model can effectively reduce synchronization and communication overhead while not requiring heavy scheduling overhead or graph-centric sequential algorithms. We then demonstrate how the hybrid execution model can be easily implemented within the BSP abstraction to preserve its simple programming interface. Finally, we evaluate our implementation of the GraphHP platform on classical BSP applications and show that it performs significantly better than the state-of-the-art BSP implementations. Our GraphHP implementation is based on Hama, but can easily generalize to other BSP platforms.