When a user scratches a hand-held rigid tool across an object surface, an acceleration signal can be captured, which carries relevant information about the surface. More importantly, such a haptic signal is complementary to the visual appearance of the surface, which suggests the combination of both modalities for the recognition of the surface material. In this paper, we present a novel deep learning method dealing with the surface material classification problem based on a Fully Convolutional Network (FCN), which takes as input the aforementioned acceleration signal and a corresponding image of the surface texture. Compared to previous surface material classification solutions, which rely on a careful design of hand-crafted domain-specific features, our method automatically extracts discriminative features utilizing the advanced deep learning methodologies. Experiments performed on the TUM surface material database demonstrate that our method achieves state-of-the-art classification accuracy robustly and efficiently.