The current works about MapReduce task scheduling with deadline constraints neither take the differences of map nor reduce task, nor the cluster's heterogeneity into account. This paper proposes an extensional MapReduce task scheduling algorithm for deadline constraints in hadoop platform: MTSD. It allows user specify a job's deadline and tries to make the job be finished before the deadline. Through measuring the node's computing capacity, a node classification algorithm is proposed in MTSD. This algorithm classifies the nodes into several levels in heterogeneous clusters.