It is witnessed that heterogeneous architectures, such as GPUs, TPUs, and FPGAs, have made complex algorithms practical in the last decade. Despite multiple efforts to study the scheduling of these parallel and complex tasks on heterogeneous architectures, the power and energy consumption of the platforms have yet to be well managed under real-time task deadlines. To establish high schedulability in heterogeneous architectures, many scheduling strategies and models, such as multi-segment selfsuspension (MSSS), have been proposed by pioneer researchers. However, directly applying this model to heterogeneous architectures with multiple CPUs and many processing elements (PEs) suffers aggravated power consumption due to the pessimism in the scheduling algorithm and the tolerance margin in the worst-case execution time (WCET) model. Therefore, this paper presents an energy-efficient real-time scheduling approach called EESchedule, which works on heterogeneous architectures with guaranteed schedulability and improved power efficiency. In EESchedule, we build a general task execution model for the general heterogeneous architectures integrating multiple CPUs and many PEs. Then, an energy-efficient real-time scheduling strategy is introduced. Next, the response time and corresponding schedulability analysis are presented for EESchedule. Finally, extensive experiments on heterogeneous NVIDIA Jetson TX2 embedded systems and GPU servers with the Intel i9-10900x CPU and RTX 3080 GPU demonstrate that the EESchedule could achieve the same schedulability with 16.8%-40.7% and 39.0%-48.2% reduced power and energy consumption in comparison with state-of-the-art scheduling algorithms.