This paper proposes controller of leader robot considering following robot with input constraints based on leader-following approach. In the previous formation control researches, it was assumed that leader and follower is same object. If leader robot drives as maximum speed that the initial position errors still remain even if following robot have same velocity as a leader. In the situation that velocity of following robot is lower than its leader robot, following robot cannot follow leader robot. Furthermore, the following robot will not be able to made formation with leader robot and keep proximity communication or sensing range. Therefore, multiple mobile robot system using leader-following method should be guaranteed range to get information each other. In this paper, Leader robot is driving to goal position using linear controller and following robot is following trajectory to be made from leader robot. We assume that following robot has input constraints to realize different performance between leader robot and following robot. We design controller of leader robot for desired goal position including the errors between formation and following robot. Thus, we propose leader robot controller considering input constraints of following robot. Finally, we were able to confirm the validity of the proposed method based on simulation results.