Heterogeneous multiprocessor systems are now widely used in industry by providing high performance and high concurrency. However, with the increasing number of computational nodes, it leads to a dramatic increase in energy consumption of heterogeneous multiprocessor systems. Most of the current research has been conducted to reduce the energy consumption by reducing the processor frequency and extending the task execution time, but these measures often lead to a significant decrease in system reliability. This article addresses the problem of energy-aware task scheduling in the case of distributed computing systems with deadline and reliability constraints.First, a time and reliability allocation model is built to assign the deadline and reliability constraints to each task, which ensures fairness among tasks. Then, a three-stage scheduling algorithm is proposed to minimize the system energy consumption. The static energy consumption is minimized by shutting down the inefficient processors.The dynamic energy consumption of the system is reduced by distributing tasks as evenly as possible on each processor through a task redistribution strategy. Finally, experimental results on real scientific workflows and randomly generated graphs show that the proposed algorithm outperforms other algorithms in terms of energy reduction.