Off-pump coronary artery bypass graft surgery outperforms the traditional on-pump surgery because the assisted robotic tools can cancel the relative motion between the beating heart and the robotic tools, which reduces post-surgery complications for patients. The challenge for the robot assisted tool when tracking the beating heart is the abrupt change caused by the nonlinear nature of heart motion and high precision surgery requirements. A characteristic analysis of 3D heart motion data through bi-spectral analysis demonstrates the quadratic nonlinearity in heart motion. Therefore, it is necessary to introduce nonlinear heart motion prediction into the motion tracking control procedures. In this paper, the heart motion tracking problem is transformed into a heart motion model following problem by including the adaptive heart motion model into the controller. Moreover, the model following algorithm with the nonlinear heart motion model embedded inside provides more accurate future reference by the quadratic term of sinusoid series, which could enhance the tracking accuracy of sharp change point and approximate the motion with sufficient detail. The experiment results indicate that the proposed algorithm outperforms the linear prediction-based model following controller in terms of tracking accuracy (root mean square).