It is essential to utilize deep-learning algorithms based on big data for the implementation of the new generation of artificial intelligence. Effective utilization of deep learning relies considerably on the number of labeled samples, which restricts the application of deep learning in an environment with a small sample size. In this paper, we propose an approach based on a generative adversarial network (GAN) combined with a deep neural network (DNN). First, the original samples were divided into a training set and a test set. The GAN was trained with the training set to generate synthetic sample data, which enlarged the training set. Next, the DNN classifier was trained with the synthetic samples. Finally, the classifier was tested with the test set, and the effectiveness of the approach for multi-classification with a small sample size was validated by the indicators. As an empirical case, the approach was then applied to identify the stages of cancers with a small labeled sample size. The experimental results verified that the proposed approach achieved a greater accuracy than traditional methods. This research was an attempt to transform the classical statistical machine-learning classification method based on original samples into a deep-learning classification method based on data augmentation. The use of this approach will contribute to an expansion of application scenarios for the new generation of artificial intelligence based on deep learning, and to an increase in application effectiveness. This research is also expected to contribute to the comprehensive promotion of new-generation artificial intelligence.