Recent advances in spatial transcriptomics have enabled the comprehensive measurement of transcriptional profiles while retaining the spatial contextual information. Identifying spatial domains is a critical step in the analysis of spatially resolved transcriptomics. Existing unsupervised methods perform poorly on this task owing to the large amount of noise and dropout events in the transcriptomic profiles. To address this problem, we first extend an unsupervised algorithm to a supervised learning method that can identify useful features and reduce noise hindrance. Second, inspired by the classical convolution in convolutional neural networks (CNNs), we designed a regular hexagonal convolution to compensate for the missing gene expression patterns from adjacent nodes. Compared with the graph convolution in graph neural networks (GNNs), our hexagonal convolution can preserve the relative spatial location information of different nodes in graph-structured data. Third, based on the hexagonal convolution, a novel hexagonal Convolutional Neural Network (hexCNN) is proposed for spatial transcriptomics classification. Finally, we compared the proposed hexCNN with existing methods on the DLPFC dataset. The results show that hexCNN achieves a classification accuracy of 87.2% and an average Rand index (ARI) of 78.2% (1.9% and 3.3% higher than those of GNNs).