Due to the anticipated future, extensive use of robots, human beings will probably share common spaces with them. The relationships between robots and humans will be conducted at close distances. Predicting people's future positions helps robots understand human behavior and react safely and naturally. In this paper, we propose a method for predicting people's positions in crossing behaviors, i.e. different trajectories people follow when they are crossing each other. We conducted a field experiment to gather various crossing behaviors of pedestrians in a shopping mall environment and analyzed them by focusing on “hot areas” spaces where people modify their trajectories for crossing. We clustered typical crossing behaviors in hot areas and modeled them using Hidden Markov Models for predictions. Our algorithm more accurately predicts the future positions of pedestrians by considering moving direction and speed.