A major challenge in EEG-based brain-computer interfaces (BCIs) is the intersession nonstationarity in the EEG data that often leads to deteriorated BCI performances. To address this issue, this letter proposes a novel data space adaptation technique, EEG data space adaptation (EEG-DSA), to linearly transform the EEG data from the target space (evaluation session), such that the distribution difference to the source space (training session) is minimized. Using the Kullback-Leibler (KL) divergence criterion, we propose two versions of the EEG-DSA algorithm: the supervised version, when labeled data are available in the evaluation session, and the unsupervised version, when labeled data are not available. The performance of the proposed EEG-DSA algorithm is evaluated on the publicly available BCI Competition IV data set IIa and a data set recorded from 16 subjects performing motor imagery tasks on different days. The results show that the proposed EEG-DSA algorithm in both the supervised and unsupervised versions significantly outperforms the results without adaptation in terms of classification accuracy. The results also show that for subjects with poor BCI performances when no adaptation is applied, the proposed EEG-DSA algorithm in both the supervised and unsupervised versions significantly outperforms the unsupervised bias adaptation algorithm (PMean).