To enhance the productivity and quality, high speed and high precision industrial robots are required. Industrial robots suffer a vibration caused by the axial torsion that adversely affects their motion control. In addition, the vibration of a joint is transfered to another joint because of the dynamic interferences with the robot manipulator. To overcome these problems, this paper proposes a new method for the link-coupled vibration suppression control for industrial robots, in which the product of inertia is considered. First, this paper shows a two-inertia model with a consideration that the product of inertia is a linear behavior. Hence, this paper proposes a new link-coupled vibration suppression control system, which consists of the speed controller and the state feedback. The effectiveness of proposed method is confirmed by the numerical simulation using a 3-DOF industrial robot model.