Electroencephalogram (EEG) classification has attracted great attention in recent years, and many models have been presented for this task. Nevertheless, EEG data vary from subject to subject, which may lead to the performance of a classifier degrades due to individual differences. To collect enough labeled data to model would address the issue, but it is often time-consuming and labor-intensive. In this paper, we propose a new multi-source transfer learning method based on domain adversarial neural network for EEG classification. Specifically, we design a domain adversarial neural network, which includes a feature extractor, a classifier, and a domain discriminator, and therefore reduce the domain shift to achieve the purpose. In addition, a unified multi-source optimization framework is constructed to further improve the performance, and the result for EEG classification is induced by the weighted combination of the predictions from multiple source domains. Experiments on three publicly available EEG datasets validate the advantages of the proposed method.