An essential requirement for performing robotic assisted surgery on a freely beating heart is a prediction algorithm which can estimate the future trajectory of the heart in the varying heart rate (HR) conditions of real surgery with a high accuracy. In this study, a hybrid amplitude modulation- (AM) and autoregressive- (AR) based algorithm was developed to enable estimating the global and local oscillations of the beating heart, raised from its major and minor physiological activities. The AM model was equipped with an estimator of the heartbeat frequency to compensate for the HR variations. The RMS of the prediction errors of the hybrid algorithm was in the range of 165–361 μm for the varying HR motion, 21% less than that of the single AM model. With the capability of providing highly accurate predictions in a wide range of HR variation, the hybrid model is promising for practical use in robotic assisted beating heart surgery. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.