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Convolutional operations can extract effective features and have been widely used in the field of deep learning. For the deficiency of convolution mainly dealing with numerical data, we propose a novel convolutional operator on granules with a set form, further we build a classifier on it. Firstly, feature granules are constructed on each single feature of a classification system by introducing neighborhood rough sets. Synchronously, decision granules are generated on the labels of samples. Secondly, feature granule vectors and weighted granule vectors are constructed from these granules, and a convolutional operation is proposed on feature granule vectors and weighted granule vectors, then a predicted granule is produced as a result of the convolutional operation. The predicted granule is compared with the decision granule, and their residual error is back propagated to the weighted granule vector for tuning its value. After multiple iterations of the granular convolutional operations and back propagation corrections, the weight of the granular vector is convergent and optimized. Furthermore, a granular classifier is designed based on the convolutional operation. The constringency of the granular convolution and the classification performance of the granular classifier are tested on some UCI datasets. Theoretical analysis and experimental results show that the granular convolution has a characteristic of fast convergence, and the granular convolutional classifier has a better classification performance.