Energy consumption minimization is one of the primary design requirements for heterogeneous distributed systems. State-of-the-art algorithms are used to study the problem of minimizing the energy consumption of a real-time parallel application with precedence constrained tasks on a heterogeneous distributed system by introducing the concept of latest finish time (LFT) to reclaim the slack time based on the dynamic voltage and frequency scaling (DVFS) energy-efficient design optimization technique. However, the use of DVFS technique alone is insufficient, and the energy consumption reduction is limited because scaling down the frequency is restricted in practice. Furthermore, these studies merely minimize energy consumption through a local energy-efficient scheduling algorithm, such as reducing the energy consumption for each task on the fixed processor, rather than a global energy-efficient scheduling algorithm, such as reducing the energy consumption for each task on different processors. This study solves the problem of minimizing the energy consumption of a real-time parallel application on heterogeneous distributed systems by using the combined non-DVFS and global DVFS-enabled energy-efficient scheduling algorithms. The non-DVFS energy-efficient scheduling (NDES) algorithm is solved by introducing the concept of deadline slacks to reduce the energy consumption while satisfying the deadline constraint. The global DVFS-enabled energy-efficient scheduling (GDES) algorithm is presented by moving the tasks to the processor slacks that generate minimum dynamic energy consumptions. Results of the experiments show that the combined NDES&GDES algorithm can save up to 36.25-55.65 percent of energy compared with state-of-the-art counterparts under different scales, parallelism, and heterogeneity degrees of parallel applications.