Despite impressive advancements in diffusion-based video editing models in altering video attributes, there has been limited exploration into modifying motion information while preserving the original protagonist's appearance and background. In this paper, we propose MotionFollower, a score-guided diffusion model for video motion editing. To introduce conditional controls to the denoising process, we propose two signal controllers, one for poses and the other for appearances, both consist of convolution blocks without involving heavy attention calculations. Further, we design a score guidance principle based on a two-branch architecture (a reconstruction and an editing branch), significantly enhancing the modeling capability of texture details and complicated backgrounds. Concretely, we enforce several consistency regularizers during the score estimation. The resulting gradients thus inject appropriate guidance to latents, forcing the model to preserve the original background details and protagonists' appearances without interfering with the motion modification. Experiments demonstrate MotionFollower's competitive motion editing ability qualitatively and quantitatively. Compared with MotionEditor, the most advanced motion editing model, MotionFollower delivers superior motion editing performance and exclusively supports large camera movements. To the best of our knowledge, MotionFollower is the first diffusion model to explore score regularization in video editing.