Recently, virtualization has become more and more important in the cloud computing to support efficient flexible resource provisioning. However, the performance interference among virtual machines may affect the efficiency of the resource provisioning. In a virtualized environment, where multiple MapReduce applications are deployed, the performance interference can also affect the performance of the Map and Reduce tasks resulting in the performance degradation of the MapReduce jobs. Then, in order to ensure the performance of the MapReduce jobs, a framework for scheduling the MapReduce jobs with the consideration of the performance interference among the virtual machines is proposed. The core of the framework is to identify the straggler tasks in a job and back up these tasks to make the backed up one overtake the original tasks in order to reduce the overall response time of the job. Then, to identify the straggler task, this paper uses a method for predicting the performance interference degree. A method for scheduling the backing-up tasks is presented. To verify the effectiveness of our framework, a set of experiments are done. The experiments show that the proposed framework has better performance in the virtual cluster compared with the current speculative execution framework.