In this paper, we propose a convolutional neural network (CoNN) for texture classification. This network has the ability to perform feature extraction and classification within the same architecture, whilst preserving the two-dimensional spatial structure of the input image. Feature extraction is performed using shunting inhibitory neurons, whereas the final classification decision is performed using sigmoid neurons. Tested on images from the Brodatz texture database, the proposed network achieves similar or better classification performance as some of the most popular texture classification approaches, namely Gabor filters, wavelets, quadratic mirror filters (QMF) and co-occurrence matrix methods. Furthermore, The CoNN classifier outperforms these techniques when its output is postprocessed with median filtering.