A mobile manipulator uses marker detection and hand-eye calibration to compensate for the performance limitation of position estimation during pick-and-place tasks. However, even if these methods are applied, an error occurs due to the limitation of camera calibration, so it is not easy to place the object in the correct position. To solve this problem, this study proposes a system that enables the manipulator to move to the correct target position based on the relationship between the estimated marker position and the motion displacement of the end-effector of the manipulator. First, the relative position between the end-effector frame and the camera frame is accurately estimated to reduce errors that occur when moving the manipulator based on the camera frame. Then, a model is built between the estimated marker position and the actual one, and the manipulator is moved to the correct position by obtaining the displacement of the manipulator according to the estimated marker position. Experiments have shown that the proposed system has a small error of less than 0.5 mm and allows the mobile manipulator to place objects in the correct position.