In this paper, we propose a new beam training framework to cope with mobility scenarios in millimeter wave communications. When a position of the mobile changes, the base-station needs to perform beam training frequently to track the time-varying channel, which leads to significant training overhead in radio resources. In order to alleviate this problem, we propose a “dedicated beam training” which serves only users under high mobility. Combined with conventional common beam training, the proposed dedicated beam training can allow the high mobility users to acquire channels with a small number of training beams exploiting the location information of the target user. The optimal selection of the training beams is formulated such that the lower bound of the angle of departure (AoD) estimate is minimized over the beam codebook indices given the estimate of the previous AoD state. Our numerical evaluation demonstrates that the proposed beam training scheme can maintain good channel estimation performance with less training overhead than the conventional beam training protocol.