MRI is capable of providing flexible soft tissue contrast and real-time guidance of interventions. Real-time information about the motion of tissues and devices is essential to provide feedback for physician and robotic control of MRI-guided interventions. In this work, a new motion prediction algorithm using MRI-based motion tracking and multi-rate Kalman filtering is proposed to provide accurate and real-time motion information. Experiments and simulations show that Kalman filtering with expectation maximization training and multi-rate data fusion is able to achieve low motion prediction error. This new algorithm has potential in providing real-time feedback information for MRI-guided interventions.