Banding or false contour is an annoying visual artifact whose impact is even more pronounced in ultra high definition, high dynamic range, and wide colour gamut visual content, which is becoming increasingly popular. Since users associate a heightened expectation of quality with such content and banding leads to deteriorated visual quality-of-experience, the area of banding removal or debanding has taken paramount importance. Existing debanding approaches are mostly knowledge-driven. Despite the widespread success of deep learning in other areas of image processing and computer vision, data-driven debanding approaches remain surprisingly missing. In this work, we make one of the first attempts to develop a deep learning based banding artifact removal method for images and name it deep debanding network (deepDeband). For its training, we construct a large-scale dataset of 51,490 pairs of corresponding pristine and banded image patches. Performance evaluation shows that deepDeband is successful at greatly reducing banding artifacts in images, outperforming existing methods both quantitatively and visually.