As the energy consumption of multi-core systems becomes increasingly prominent, meeting the time constraints while reducing as much as possible system energy consumption is still an urgent problem in real-time energy-aware scheduling in multi-core system. Most existing works have assumptions on priori information of real-time tasks, but in real applications the tasks’ property be received only when the tasks arrive. Therefore, based on the general task model with no priori to tasks’ properties, this paper proposes a global EDF-based on-line energy-aware scheduling algorithm for hard real-time tasks in multi-core system. The proposed algorithm can reduce the execution speed of task in multi-core system and reach a reasonable compromise between real-time constraints and energy savings, as it introduces a speed scale factor for utilizing the slack time and combines dynamic power management with dynamic voltage/frequency scaling techniques. The algorithm implements dynamic voltage/frequency scaling only in each context switch time and task completion time, with the smaller computational complexity, and easier to be included in real-time operating system. Experimental results show that the algorithm can be well applied to different kinds of dynamic voltage/frequency scaling on chip, and compared with Global EDF algorithm, it gain more energy savings in all cases, which can improve energy savings about 15% to 20% at most and about 5% to 10% at least.