Objective: This paper targets a major challenge in developing practical EEG-based brain-computer interfaces (BCIs): how to cope with individual differences so that better learning performance can be obtained for a new subject, with minimum or even no subject-specific data? Methods: We propose a novel approach to align EEG trials from different subjects in the Euclidean space to make them more similar, and hence improve the learning performance for a new subject. Our approach has three desirable properties: 1) it aligns the EEG trials directly in the Euclidean space, and any signal processing, feature extraction and machine learning algorithms can then be applied to the aligned trials; 2) its computational cost is very low; and, 3) it is unsupervised and does not need any label information from the new subject. Results: Both offline and simulated online experiments on motor imagery classification and event-related potential classification verified that our proposed approach outperformed a state-of-the-art Riemannian space data alignment approach, and several approaches without data alignment. Conclusion: The proposed Euclidean space EEG data alignment approach can greatly facilitate transfer learning in BCIs. Significance: Our proposed approach is effective, efficient, and easy to implement. It could be an essential pre-processing step for EEG-based BCIs.