Brain-computer interface (BCI) research has attracted worldwide attention and has been rapidly developed. As one well-known non-invasive BCI technique, electroencephalography (EEG) records the brain's electrical signals from the scalp surface area. However, due to the non-stationary nature of the EEG signal, the distribution of the data collected at different times or from different subjects may be different. These problems affect the performance of the BCI system and limit the scope of its practical application. In this study, an unsupervised deep-transfer-learning-based method was proposed to deal with the current limitations of BCI systems by applying the idea of transfer learning to the classification of motor imagery EEG signals. The Euclidean space data alignment (EA) approach was adopted to align the covariance matrix of source and target domain EEG data in Euclidean space. Then, the common spatial pattern (CSP) was used to extract features from the aligned data matrix, and the deep convolutional neural network (CNN) was applied for EEG classification. The effectiveness of the proposed method has been verified through the experiment results based on public EEG datasets by comparing with the other four methods.