This paper proposes velocity obstacle (VO) considering collision prediction time for a mobile robot with a non-holonomic constraint. VO is a useful trajectory planning method that takes into account obstacle avoidance. Therefore, various VO-based trajectory planning methods have been reported. VO is defined as the velocity areas where there is a possibility of collision. VO-based methods select the velocity commands outside VO for collision avoidance. The proposed method clarified the condition for velocity selection inside VO considering kinematic constraint. In addition, the dynamic weight coefficient considering collision prediction time is developed. By using the evaluation function including the velocity conditions and dynamic weight, the velocity command is selected from the velocity candidates both inside and outside VO. In the simulation and experiments, the effectiveness of trajectory planning under multiple obstacles by using the proposed method was verified.