The use of transfer learning in brain-computer interfaces (BCIs) has potential applications. As electroencephalogram (EEG) signals vary among different paradigms and subjects, existing EEG transfer learning algorithms mainly focus on the alignment of the original space. They may not discover hidden details owing to the low-dimensional structure of EEG. To effectively transfer data from a source to target domain, a multi-manifold embedding domain adaptive algorithm is proposed for BCI. First, we aligned the EEG covariance matrix in the Riemannian manifold and extracted the characteristics of each source domain in the tangent space to reflect the differences between different source domains. Subsequently, we mapped the extracted characteristics to the Grassmann manifold to obtain a common feature representation. In domain adaptation, the geometric and statistical attributes of EEG data were considered simultaneously, and the target domain divergence matrix was updated with pseudo-labels to maximize the inter-class distance and minimize the intra-class distance. Datasets generated via BCIs were used to verify the effectiveness of the algorithm. Under two experimental paradigms, namely single-source to single-target and multi-source to single-target, the average accuracy of the algorithm on three datasets was 73.31% and 81.02%, respectively, which is more than that of several state-of-the-art EEG cross-domain classification approaches. Our multi-manifold embedded domain adaptive method achieved satisfactory results on EEG transfer learning. The method can achieve effective EEG classification without a same subject's training set.