A railway wheelset experiences the problem of hunting motion above a critical speed, which is known as a flutter-type self-excited oscillation due to a nonconservative contact force acting between wheels and rails. In order to improve the running performance on the straight rail, the utilization of a gyroscopic damper is proposed. The validity of the proposed method is theoretically and experimentally confirmed for the increase of the critical speed of the hunting motion. In this paper, more study considering constant curve was done.