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Recently, tactile sensing has attracted great interest in robotics, especially for facilitating exploration of unstructured environments and effective manipulation. A detailed understanding of the surface textures via tactile sensing is essential for many of these tasks. Previous works on texture recognition using camera based tactile sensors have been limited to treating all regions in one tactile image or all samples in one tactile sequence equally, which includes much irrelevant or redundant information. In this paper, we propose a novel Spatio-Temporal Attention Model (STAM) for tactile texture recognition, which is the very first of its kind to our best knowledge. The proposed STAM pays attention to both spatial focus of each single tactile texture and the temporal correlation of a tactile sequence. In the experiments to discriminate 100 different fabric textures, the spatially and temporally selective attention has resulted in a significant improvement of the recognition accuracy, by up to 18.8%, compared to the non-attention based models. Specifically, after introducing noisy data that is collected before the contact happens, our proposed STAM can learn the salient features efficiently and the accuracy can increase by 15.23% on average compared with the CNN based baseline approach. The improved tactile texture perception can be applied to facilitate robot tasks like grasping and manipulation.