The knowledge of potentially druggable binding sites on proteins is an important preliminary step towards the discovery of novel drugs. The computational prediction of such areas can be boosted by following the recent major advances in the deep learning field and by exploiting the increasing availability of proper data. In this paper, a novel computational method for the prediction of potential binding sites is proposed, called DeepSurf. DeepSurf combines a surface-based representation, where a number of 3D voxelized grids are placed on the protein's surface, with state-of-the-art deep learning architectures. After being trained on the large database of scPDB, DeepSurf demonstrates superior performance on two diverse testing datasets, by surpassing all its main deep learning-based competitors.