As people become more aware of the emotion detection and fifth generation (5G) technology, emotion-aware mobile computing has become a hot issue in the affective computing systems. Emotion-aware mobile computing utilizes mobile and computing technology to detect the affective state of a person. It is a new active research area and will bring many attractive applications and services with the development of 5G. Emotion-aware mobile computing has two main veins: analysis and computation. With the support of big data and cloud computing technology, mobile users are able to obtain better performance in terms of resource intensive service. The whole process of emotion-aware mobile computing requires data collection, data transmission, data analysis, data cognition, and emotion-aware action feedback. In order to detect the accurate emotion, massive data are required to be processed in each step. Therefore, the energy consumption is not an ignorable issue in this technology. In this paper, a framework of energy efficient emotion-aware mobile computing system is proposed. It considers the energy saving from both local user part and remote data centers part. In the local user part, the energy efficient data transmission approach is introduced while in the remote data centers part, the renewable energy based geo-distributed data centers are considered. The results from the analysis demonstrate that the proposed framework is useful to provide energy saving while keeping quality of service (QoS).