In this paper, we present a novel cross-job framework for MapReduce scheduling, which aims to minimize the total processing time of a sequence of related jobs by combining reduce and map phases of two consecutive jobs and streaming data between them. The proposed framework has the following desirable properties: (1) It can accelerate the execution of a sequence of related MapReduce jobs by achieving a good tradeoff between data locality and parallelism. (2) It can support all the existing MapReduce applications with no changes to their source code. (3) It is a general framework, which can work with different scheduling algorithms. We built a new MapReduce runtime system called cross-job Hadoop by integrating the proposed cross-job framework into Hadoop. We conducted extensive experiments to evaluate its performance using PageRank and an Apache Pig application. Our experimental results show that the cross-job Hadoop can significantly reduce both the total processing time of a job sequence and the size of data transferred over the network.