Path following control problem has been treated in recent years. In past studies, the velocity of the plant is considered as constant value. However, the velocity of the plant must be controlled so as to reduce traveling time. In this paper, velocity control in path following problem is discussed by using optimal control. Since reaching time from the start point to the terminal point is used as a cost, we can obtain good acceleration and deceleration input. Since constraints of path following are included in the optimal control problem, we can achieve not only optimization of the cost but also path following. The effectiveness of the proposed method is examined by numerical examples with a path of non-constant curvature.