MapReduce, a popular programming model for processing data-intensive tasks, has achieved great success in a wide range of applications such as search indexing, social network mining, collaborative recommendation, and spam detection. However, the ability of MapReduce is limited in two respects by its default schedulers. First, it does not support concurrent services sharing a cloud datacenter and second, it fails to guarantee response time for deadline-constrained services. This paper proposes the Paused Rate Monotonic (PRM) algorithm for scheduling hard real-time tasks on a MapReduce-based cloud. The scheduling performance is analyzed theoretically. We prove a bound on cluster utilization, which can be used as a sufficient condition to test whether a given task set can be scheduled. Both the theoretical analysis and experimental evaluation show that the PRM algorithm outperforms traditional real-time ones by improving the probability that a real-time task set can be scheduled on a MapReduce-based cloud.