Dense local trajectories have been successfully used in action recognition. However, for most actions only a few local motion features (e.g., critical movement of hand, arm, leg etc.) are responsible for the action label. Therefore, highlighting the local features which are associated with important motion parts will lead to a more discriminative action representation. Inspired by recent advances in sentence regularization for text classification, we introduce a Motion Part Regularization framework to mine for discriminative groups of dense trajectories which form important motion parts. First, motion part candidates are generated by spatio-temporal grouping of densely extracted trajectories. Second, an objective function which encourages sparse selection for these trajectory groups is formulated together with an action class discriminative term. Then, we propose an alternative optimization algorithm to efficiently solve this objective function by introducing a set of auxiliary variables which correspond to the discriminativeness weights of each motion part (trajectory group). These learned motion part weights are further utilized to form a discriminativeness weighted Fisher vector representation for each action sample for final classification. The proposed motion part regularization framework achieves the state-of-the-art performances on several action recognition benchmarks.