MapReduce can speed up the execution of jobs operating over big data. A MapReduce job can be divided into a number of map and reduce tasks by a well determined division manner on its processing data. In a cloud computing system, multiple MapReduce jobs may be submitted together to compete for the computing resources of the system. When a job has a particular performance requirement (e.g. execution deadline), the appropriate computing resources must be kept for executing the map/reduce tasks of the job; otherwise, the performance requirement cannot be satisfied. Several deadline-constrained MapReduce schedulers have been proposed, but most of them are not aware of the performance influence over existing tasks. We propose a deadline-constrained and influence-aware MapReduce scheduler which combines the following three factors: (1) relaxed data locality, (2) performance influence over existing tasks, and (3) coordinating allocation contention. We first adopt the data-locality criterion to make a tentative allocation plan. By verifying the data-locality allocation plan, if some new tasks severely affect existing tasks or the deadline requirements of some new tasks are not satisfied, the data-locality allocation plan will be modified by re-allocating some new tasks. To optimize the computing resource usage, the solution of a well-known network graph problem: minimum cost maximum-flow (MCMF) is applied to perform the modification of the data-locality allocation plan. A heuristic algorithm is also presented to suppress the complexity of MCMF problem. In addition to meeting the deadline requirements of new jobs, the final allocation plan also considers the performance influence over existing jobs. Finally, we conduct the performance analysis to demonstrate the performance of our proposed MapReduce scheduler using various performance metrics.