Single-image super-resolution (SR) is one of the most important and challenging issues in image processing. To produce a high-resolution image from a low-resolution image, one of the conventional approaches is to leverage regularization to overcome the limitations caused by the modeling. However, conventional regularizers such as total variation always neglect the high-level structures in the data. To overcome the drawback, we propose to explore the underlying information for the images with structured edges by using directional total variation. An alternating direction method of a multiplier-based algorithm is presented to effectively solve the resulting optimization problem. Computer simulations on several texture images such as a leaf image have been used to demonstrate the effectiveness and improvement of the proposed method on SR reconstruction, both qualitatively and quantitatively. Furthermore, the effect of parameter selection is also discussed for the proposed method.