Disclosed is a system for controlling the position of a floating rig that permits holding the rig at a position optimum to an excavation riser even if a position signal of the floating rig is not received, provided that the angles of inclination at the upper and lower ends of the riser are detected. In the method of controlling the position of a floating rig, the floating rig 10 is joined to a well head 14 at the sea bottom by an excavation riser 16, and the rig 10 is driven to a corrected position by thrusters or a combination of thrusters and a propulsion system. A neural network is allowed to learn in advance the position information of the floating rig accompanying the behaving characteristics of the excavation riser. The angles of inclination at the upper and lower ends of the excavation riser are detected and a signal represent of the detected angles is supplied to the neural network so as to permit the neural network to output the information on the correction of the present position of the floating rig. Based on the position information, the correcting information that permits diminishing the angles of inclination at the upper and lower ends of the riser is calculated so as to automatically control the position of the floating rig. Where the position information of the floating rig has ceased to be received, the angles of inclination at the upper and lower ends of the excavation riser that are to be detected are supplied to the position estimating section of the rig based on the algorithm of Kalman filter so as to estimate the rig position and, thus, to perform the position control.