With the increasing availability and scale of graph data from Web 2.0, graph partitioning becomes one of efficient preprocessing techniques to balance the computing workload. Since the cost of partitioning the entire graph is strictly prohibitive, there are some recent tentative works towards streaming graph partitioning which can run faster, be easily paralleled, and be incrementally updated. Unfortunately, the experiments show that the running time of each partitioning is still unbalanced due to the variation of workload access pattens during the supersteps. In addition, the one-pass streaming partitioning result is not always satisfactory for the algorithms' local view of the graph. In this paper, we present LogGP, a log-based graph partitioning system that records, analyzes and reuses the historical statistical information to refine the partitioning result. LogGP can be used as a middle-ware and deployed to many state-of-the-art paralleled graph processing systems easily. LogGP utilizes the historical partitioning results to generate a hyper-graph and uses a novel hyper-graph streaming partitioning approach to generate a better initial streaming graph partitioning result. During the execution, the system uses running logs to optimize graph partitioning which prevents performance degradation. Moreover, LogGP can dynamically repartition the massive graphs in accordance with the structural changes. Extensive experiments conducted on a moderate size of computing cluster with real-world graph datasets demonstrate the superiority of our approach against the state-of-the-art solutions.