The morphology of galaxies is closely related to the formation and evolution of galaxies, and its morphological classification is a significant part of the follow-up research of galaxy astronomy. With the emergence of massive astronomical observation data, the automatic analysis of astronomical data has attracted more and more attention. To solve this problem, the advanced deep learning backbone network EfficientNetV2 is utilized to analyze the effects of different attention mechanism types and usage nodes on network performance, and an improved algorithm model named EfficientNetV2-S-Triplet7 is constructed to realize automatic classification of galaxy morphology. More than 240 thousand photometric images from Galaxy Zoo 2 are used as initial data for experimental tests. In the process of data preprocessing, image enhancement methods such as size jittering, flipping and color distortion are adopted to solve the problem of image number imbalance. After conducting comparative experiments on the same series of classic and cutting-edge deep learning algorithms AlexNet, RegNet, MobileNetV2 and ResNet-34, it is concluded that the EfficientNetV2-S-Triplet7 algorithm has the best test results in classification accuracy, recall and F1-score. In 9375 test images, the three index values can reach 89.03%, 90.21% and 89.93%, respectively, and the precision can reach 89.69%, ranking the third among other models. The results show that EfficientNetV2-S-Triplet7 algorithm can be effectively applied to the morphological classification of large-scale galaxy data.