Many algorithms on subgraph mining have been proposed. However, the number of frequent subgraphs generated by these algorithms may be too large to be effectively explored by users, especially when the support threshold is low. In this paper, a new problem of mining frequent jump patterns from graph databases is proposed. Mining frequent jump patterns can dramatically reduce the number of output graph patterns and still capture interesting graph patterns. Futhermore, jump patterns are robust against noise and dynamic changes in data. However, this problem is challenging due to the underlying complexity associated with frequent subgraph mining as well as the absence of Apriori property for jump patterns. By exploring the properties of jump patterns, two novel effective pruning techniques are proposed: Internal-Extension-Based pruning and external-extension-based pruning. Based on the proposed pruning techniques, an efficient algorithm GraphJP is presented for this new problem. It has been theoretically proven that the novel pruning techniques and the proposed algorithm are correct. Extensive experimental results demonstrate that the novel pruning techniques are effective in pruning the unpromising parts of search space, and GraphJP is efficient and scalable in mining frequent jump patterns.