In this paper, we propose a cooperative control method of transporting a single object utilizing a leader-follower type multiple robot system with loose handling. It is advantageous for a desired trajectory or an external operation command to be given only to a leader robot, and follower robots estimate the trajectory of the leader using the forces information from the object during transportation. If the follower robots hold the object being transported rigidly, the forces generated by the leader reach to the followers correctly and immediately via the object. However, the forces include delay with loose handling and cooperative transportation will fail with a traditional algorithm. First, we specify the problem that occurs in the case of the loose handling accoriding to the traditional method. Next, we propose the estimation algorithm of the leader trajectory for the followers with the loose handling. Finally, cooperative transportation simulations and experimentations are presented. In this validation, multiple robots with 6-DOF manipulators on non-holonomic vehicles are used, where manipulators have a hook as an end-effector to suspend the object being transoprted to imitate a crane system.