Our knowledge of galaxy creation and evolution has significantly improved in recent years because of the substantial advancements made in the classification of galaxy morphology using machine learning techniques. Nevertheless, the vast amount of unlabeled astronomical image data restricts the application of these techniques, and it is expensive to manually label enormous volumes of astronomical data. Current semi-supervised approaches have used pseudo-labeling and consistency regularization to get good results. However, many pseudo-labels are underutilized because of their excessively high confidence levels. Furthermore, confirmation bias in the model may result from the overconfidence commonly seen in softmax outputs, which is usually disregarded in current research. In order to decrease confirmation bias throughout the learning process, this study introduces uncertainty quantification. Specifically, the suggested approach fully utilizes pseudo-labeled data by using distinct training procedures according to different confidence levels. This method lowers errors brought on by the model’s overconfidence while simultaneously improving the quality of pseudo-labels. Results from experiments show that our approach performs well on the Galaxy Zoo 2 data set and the Galaxy10 DECaLS data set. In particular, our approach obtains an accuracy of 76.8% on the Galaxy10 DECaLS data set, which contains 2000 labeled samples, while fully supervised approaches only achieve 70.8%. In comparison to the supervised approach, our strategy lowers the error rate by 32.34% for the 1000 labeled samples in the Galaxy Zoo 2 data set. Our method accomplishes accurate categorization of galaxy morphology by using a large amount of unlabeled data and a small amount of labeled data. The public can get the source code at https://github.com/CZSGC/SSLGMCBDEUE.