When a drilling riser is operated, tension is applied to maintain configuration of the riser and protect it from collapse. In the emergency condition, for example drift off or drive off of drilling vessel, the riser is disconnected at top of the BOP which is placed on the sea floor. When disconnected, the riser starts to lift and recoil, and if the tension is not properly reduced the riser hits the vessel and destroy both the vessel and riser. If the tension is reduced too fast, riser can not reach the vessel and riser drops on to the sea floor and destroyed. An anti-recoil system is necessary to protect the riser and vessel from destruction and make the catching successful. In this research response prediction system of disconnected riser is developed considering coupled response of riser and dynamic response of internal and external fluid. Vessel heave motion prediction system is also developed. An algorithm is developed to search catching timing from the both predictions of riser motion and vessel heave motion. To achieve successful catching, the catching timing must satisfy catching condition of no relative displacement, velocity and acceleration. Once the catching timing is found, riser disconnection timing is determined from the predicted riser motion. Feedback control is employed at the final stage of catching to adjust and absorb modeling errors and prediction errors and secure successful catching. Effectiveness of the developed algorithm is verified by simulation calculation.