Beating-heart surgery is not currently possible for most surgical procedures as it requires superhuman skill to manually track the heart's motion while performing a surgical task. However, if a surgical tool could track the motion of the point of interest (POI) on the heart, then, with respect to the surgical tool tip the POI would appear stationary. Such a system can be created with a teleoperated surgical robot that is controlled to track the combination of the heart's and the surgeon's motion, as input through a separate user console. To develop such a system, the motion of the heart is found in ultrasound images where the image acquisition introduces delays of approximately 40 ms and image processing further increases this delay. Directly using this delayed position measurement in the feedback control loop can lead to instability and poor tracking. The generalized predictive controller used in this work compensates for this time delay despite large disturbances with velocities up to 210 mm/s and accelerations up to 3800 mm/s2caused by the moving heart.