Competitive learning attracts increasingly attention in digital game-based learning. However, since the limitation of social competition in application, there is a need to investigate other competitive models. In this paper, a self-competition model is emphasized, and a My-Avatar system with self-competition model is developed to further investigate students' preference on the choice between self-competition and peer-competition. The result revealed that over half of participants (63%) preferred the peer-competition version and fewer (37%) participants preferred the self-competition version. The major reasons why they preferred the competition versions were discussed.