Outdoor videos sometimes contain unexpected rain streaks due to the rainy weather, which bring negative effects on subsequent computer vision applications, e.g., video surveillance, object recognition and tracking, etc. In this paper, we propose a directional regularized tensor-based video deraining model by taking into consideration the arbitrary direction of rain streaks. In particular, the sparsity of rain streaks in spatial and derivative domains, the spatiotemporal sparsity and low-rank property of video background are incorporated into the proposed method. Different from many previous methods under the assumption of vertically falling rain streaks, we consider a more realistic assumption that all the rain streaks in a video fall in an approximately similar arbitrary direction. The resulting complicated optimization problem will be effectively solved through an alternating direction method. Comprehensive experiments on both synthetic and realistic datasets have demonstrated the superiority of the proposed deraining method.