The Anatomical Therapeutic Chemical (ATC) classification system, designated by the World Health Organization Collaborating Center (WHOCC), has been widely used in drug screening, repositioning, and similarity research. The ATC classification system assigns different codes to drugs according to the organ or system on which they act and/or their therapeutic and chemical characteristics. Correctly identifying the potential ATC codes for drugs can accelerate drug development and reduce the cost of experiments. Several classifiers have been proposed in this regard. However, they lack of ability to learn basic features from sparsely known drug-ATC code associations. Therefore, there is an urgent need for novel computational methods to precisely predict potential drug-ATC code associations in multiple levels of the ATC classification system based on known associations between drugs and ATC codes. In this paper, we provide a novel end-to-end model, so-called RNPredATC, to predict potential drug-ATC code associations in five ATC classification levels. RNPredATC can extract dense feature vectors from sparsely known drug-ATC code associations and reduce the impact from the degradation problem by a novel deep residual learning. We extensively compare our method with some state-of-the-art methods, including NetPredATC, SPACE, and some multi-label-based methods. Our experimental results show that RNPredATC achieves better performances in five-fold and ten-fold cross validations. Furthermore, the visualization analysis of hidden layers and case studies of predicted associations at the fifth ATC classification level confirm that RNPredATC can effectively identify the potential ATC codes of drugs.