In this paper, a control method of robots for cooperative human-robot handling of an object is investigated. We propose estimating human motion using the minimum jerk model for smooth cooperation. Using a nonlinear least-squares method, we identify two parameters of a minimum-jerk trajectory of a human hand in real time. The estimated position of the human hand is used to determine the desired position of the end-effector of the manipulator in virtual compliance control. Motion estimation enables robots to coordinate actively even for unknown trajectories of manipulated objects that human partners intend. We implemented the proposed method on an industrial manipulator with a force sensor. In experiments of cooperative manipulation of a rubber pipe, the motion estimation improved human feeling in coordination. The improvement was quantitatively evaluated from the viewpoint of “unnecessary energy transfer.”