In this paper, dual-task performance assessment robot (DAR) using projection is developed. Falling is a common problem in the growing elderly population. Fall-risk assessment systems have proven to be helpful in community-based fall prevention programs. One of the risk factors of falling is the deterioration of a person's dual-task performance. For example, gait training, which enhances both motor and cognitive functions, is a multi-target stepping task (MTST), in which participants step on assigned colored targets. To evaluate the dual-task performance during MTST in human living space, projection mapping and robot navigation to maintain a safe distance from the participant are key technologies. Projection mapping is used to evaluate the long-distance dual-task performance, where MTST images are displayed on the floor by the moving DAR. To evaluate the accuracy of the projected target position, experiments for MTST projection using the moving DAR and video analysis are carried out. Additionally, to verify the validity of the MTST by the moving DAR at a constant speed, experiments with several young participants are carried out.