Data centers for cloud computing must accommodate numerous parallel task executions simultaneously. Therefore, data centers have many virtual machines (VMs). Minimizing the scheduling length of parallel task sets becomes a critical requirement in cloud computing systems. In this study, we propose an efficient priority and relative distance (EPRD) algorithm to minimize the task scheduling length for precedence constrained workflow applications without violating the end-to-end deadline constraint. This algorithm consists of two processes. First, a task priority queue is established. Then, a VM is mapped for a task in accordance with its relative distance. The proposed method can effectively improve VM utilization and scheduling performance. Extensive rigorous experiments based on randomly generated and real-world workflow applications demonstrate that the resource reduction rate and scheduling length of the EPRD algorithm significantly surpass those of existing algorithms.