Rain removal from a single image is an important issue in the fields of outdoor vision. Rain, a kind of bad weather that is often seen, usually causes complex local intensity changes in images and has negative impact on vision performance. Many existing rain removal approaches have been proposed recently, such as some dictionary learning-based methods and layer decomposition-based methods. Although these methods can improve the visibility of rain images, they fail to consider the intrinsic directional and structural information of rain streaks, thus usually leave undesired rain streaks or change the background intensity of rain-free region significantly. In the paper, we propose a simple but efficient method to remove rain streaks from a single rainy image. The proposed method formulates a global sparse model that involves three sparse terms by considering the intrinsic directional and structural knowledge of rain streaks, as well as the property of image background information. We employ alternating direction method of multipliers (ADMM) to solve the proposed convex model which guarantees the global optimal solution. Results on a variety of synthetic and real rainy images demonstrate that the proposed method outperforms two recent state-of-the-art rain removal methods. Moreover, the proposed method needs no training and requires much less computation significantly.