Heart motion tracking for radiation therapy treatment planning can result in effective motion management strategies to minimize radiation-induced cardiotoxicity. However, automatic heart motion tracking is challenging due to factors that include the complex spatial relationship between the heart and its neighboring structures, dynamic changes in heart shape, and limited image contrast, resolution, and volume coverage. In this study, we developed and evaluated a deep generative shape model-driven level set method to address these challenges. The proposed heart motion tracking method makes use of a heart shape model that characterizes the statistical variations in heart shapes present in a training data set. This heart shape model was established by training a three-layered deep Boltzmann machine (DBM) in order to characterize both local and global heart shape variations. During the tracking phase, a distance regularized level-set evolution (DRLSE) method was applied to delineate the heart contour on each frame of a cine MRI image sequence. The trained shape model was embedded into the DRLSE method as a shape prior term to constrain an evolutional shape to reach the desired heart boundary. Frame-by-frame heart motion tracking was achieved by iteratively mapping the obtained heart contour for each frame to the next frame as a reliable initialization, and performing a level-set evolution. The performance of the proposed motion tracking method was demonstrated using thirty-eight coronal cine MRI image sequences.