Abstract The existing snow/rain removal methods often fail for heavy snow/rain and dynamic scene. One reason for the failure is due to the assumption that all the snowflakes/rain streaks are sparse in snow/rain scenes. The other is that the existing methods often can not differentiate moving objects and snowflakes/rain streaks. In this paper, we propose a model based on matrix decomposition for video desnowing and deraining to solve the problems mentioned above. We divide snowflakes/rain streaks into two categories: sparse ones and dense ones. With background fluctuations and optical flow information, the detection of moving objects and sparse snowflakes/rain streaks is formulated as a multi-label Markov Random Fields (MRFs). As for dense snowflakes/rain streaks, they are considered to obey Gaussian distribution. The snowflakes/rain streaks, including sparse ones and dense ones, in scene backgrounds are removed by low-rank representation of the backgrounds. Meanwhile, a group sparsity term in our model is designed to filter snow/rain pixels within the moving objects. Experimental results show that our proposed model performs better than the state-of-the-art methods for snow and rain removal.