This paper describes the development of a controller that enables trajectory control and vibration control. The controller performance was verified the using a 3D 2-link, flexible manipulator. On trajectory control using inverse kinematics, it was confirmed that the deflection due to its own weight deteriorated the track following performance. The vibration component of the resonance frequency of the flexible manipulator was generated, and the tip position accuracy is deteriorated. Using the results of control experiments based on the inverse kinematics, the system is identified and then created an inverse system for simultaneous control of trajectory control and vibration control. The target trajectories were the three joint angles. Finally, it was demonstrated through experiments on actual manipulator, that the system could sufficiently follow the ideal trajectory and suppress link vibrations.