The research of underwater sonar image classification is beneficial to the development of marine resources. In recent years, deep neural networks have achieved great success in the fields of image classification and image recognition. However, deep neural networks require a large amount of training data. Due to the difficulty of obtaining sonar image datasets, the existing public sonar datasets are generally small, and sonar image classification can be regarded as a small sample problem. To solve this problem, we designed a deep adaptive sonar image classification network (DASCN) based on deep learning and domain adaptation. The feature extraction module in DASCN extracts multiscale features of images; the attention module learns the importance of different channel features; and the domain adaptation module reduces the difference between the source domain and the target domain. It is worth noting that our DASCN does not require a large number of training samples, and sonar images used for training do not need to be labeled. As demonstrated in comprehensive experiments, the classification accuracy of the DASCN model reached 89.4% on the sonar image dataset. Our DASCN achieves unsupervised accurate classification of small sample sonar images. In addition, our DASCN has good classification results on the Office-31 dataset and the Office Home dataset and has good generalization performance.