Non-rigid structure from motion (NRSfM) is a fundamental problem of computer vision. Recently, it has been shown that incorporating shape alignment in NRSfM can improve the performance significantly compared with the other algorithms, which do not consider shape alignment. However, realizing this idea was at a cost of a heavy, complicated process, which limits its usefulness and possible extensions. In this paper, we propose a novel regression framework for NRSfM, of which the variables (3D shapes) are regularized based on their aligned shapes. We show that this can be casted into an unconstrained problem or a problem with simple bound constraints, which can be efficiently solved by existing solvers. This framework can be easily integrated with numerous existing models and assumptions, such as orthographic or perspective camera models, occlusion, low-rank assumption, smooth deformations, and so on, which makes it more practical for various real situations. The experimental results show that the proposed method gives competitive result to the state-of-the-art methods for orthographic projection with much less time complexity and memory requirement, and outperforms the existing methods for perspective projection.