The big.LITTLE architecture has been extensively integrated into smart mobile devices for better performance and higher energy efficiency. However, the desired energy savings obtained by the big.LITTLE architecture is not sufficiently achieved because the LITTLE cores are not fully utilized while running real-time user applications. In this study, an energy efficient big.LITTLE core assignment algorithm is proposed to reduce the energy consumption of the mobile device by utilizing the LITTLE core as much as possible while guaranteeing the real-time performance of the mobile application. By applying the proposed multi-core assignment technique on a real test-bed of an off-the-shelf smartphone, we prove that the proposed technique can improve the energy saving effect while guaranteeing real-time performance. The energy efficiency of the proposed scheme is compared with that of the legacy scheduler in various environments. In addition, we propose a machine learning-based method to predict the expected processing time more accurately for a task before assigning to one of multi-cores. The presented prediction method is expected to reduce the chances of missing a deadline when employed on the proposed multi-core assignment scheme. INDEX TERMS energy conservation, asymmetric multi-cores, mobile devices, scheduling, real-time systems