Modern Magnetic Resonance Imaging (MRI) methods now allow the rapid acquisition of images with an excellent tissue contrast and high spatial resolution. Complex organ deformations can thus be estimated using image registration techniques applied to anatomical information. This opens great perspectives for the use of MRI to retroactively target an interventional procedure in mobile organs in real-time. For this purpose, both the update time and the latency of the motion information are two key points. In the current paper, the organ deformation is estimated on a voxel-by-voxel basis and a Kalman predictor is used to compensate for the residual latency. The implementation benefitted from the parallel architecture of Graphical Processing Units (GPU) for accelerating computation times. The efficiency and the potential of the method to anticipate organ displacements in real-time was evaluated on the abdomen of twelve free-breathing volunteers. The deformation of both kidney and liver could be updated with a rate of 10 Hz over sustained periods of several minutes, and the employed Kalman predictor reduced the tracking error in average by 30 %.