Abstract: As efficient energy management emerges as an important issue for reliable and green computing, energy-aware scheduling approach is regarded as a promising way since it is practical and low-cost. At present, there exist large challenges in the area of energy-aware scheduling for dependent tasks in grid computing system, because the precedence constraints of applications, massive data transmission, system heterogeneity and the conflict of multiple scheduling indicators should be balanced. In this paper, taking into account all the above factors, we propose ESGDT (energy-efficient scheduling of grid dependent task) algorithm, which aims to reduce energy consumption while optimizing execution time for applications. ESGDT algorithm reduces data transfer time and communication energy consumption through task duplication and progressive ratio metric, and considers complex data dependent relationship between tasks. It also considers the static power of processing element through dynamic power management technique following the trends of chip miniaturization and multi-core technology. Moreover, the condition of task duplication, the computation method of progressive ratio metric, and the rule of task adjustment all properly consider two conflicting scheduling indicators——time and energy. ESGDT algorithm also focuses on dynamic and adaptive scheduling issues in total heterogeneous system. Simulation experiments demonstrate that ESGDT algorithm could reduce more energy consumption while not influencing scheduling performance than HEFT, EETDS and HEADUS algorithms.