This paper presents a health promotion system with robot partner for elderly care. Aging society in Japan has been a big serious problem. The number of caregivers is not enough in the current situation and is not expected to substantially increase in future. Hence, comprehensive care and health promotion should be provided to heighten awareness about health. In this study, we built a daily exercise support system with a robot partner utilized as an exercise instructor. Moreover, we propose a human-robot communication model based on self-serving bias. In the experiment, we conduct a demonstration experiment and interview survey to discuss the validity of the communication model.