This article describes a dementia prevention system for the elderly based on a brain twister game in a tablet device. In this system, a software agent is incorporated into the tablet device, and has dialogic interactions with users (elderly people) based on the concept of Human-Agent Interaction (HAI) in order to reduce the users' psychological resistance to the system and maintain or improve their interest in the game. Several experiments and subjective evaluations for elderly people are conducted to evaluate the basic characteristics of the proposed system and investigate the impact of the system on the effect for preventive care.