Classification of galaxy morphology is a hot issue in astronomical research. Although significant progress has been made in the last decade in classifying galaxy morphology using deep learning technology, there are still some deficiencies in spatial feature representation and classification accuracy. In this study, we present a multiscale convolutional capsule network (MSCCN) model for the classification of galaxy morphology. First, this model improves the convolutional layers using a multibranch structure to extract the multiscale hidden features of galaxy images. In order to further explore the hidden information in the features, the multiscale features are encapsulated and fed into the capsule layer. Second, we use a sigmoid function to replace the softmax function in dynamic routing, which can enhance the robustness of MSCCN. Finally, the classification model achieves 97 per cent accuracy, 96 per cent precision, 98 per cent recall, and 97 per cent F1-score under macroscopic averaging. In addition, a more comprehensive model evaluation was accomplished in this study. We visualized the morphological features for the part of sample set that used the t-distributed stochastic neighbour embedding (t-SNE) algorithm. The results show that the model has a better generalization ability and robustness, and it can be effectively used in the galaxy morphological classification.