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Brain computer interface (BCI) utilizes brain signals to help users interact with external devices directly. EEG is one of the most commonly used techniques for brain signal acquisition in BCI. However, it is notoriously difficult to build a generic EEG recognition model due to significant non-stationarity and subject-to-subject variations, and the requirement for long time training. Transfer learning (TL) is particularly useful because it can alleviate the calibration requirement in EEG-based BCI applications by transferring the calibration information from existing subjects to new subject. To take advantage of geometric properties in Riemann manifold and joint distribution adaptation, a manifold embedded transfer learning (METL) framework was proposed for motor imagery (MI) EEG decoding. First, the covariance matrices of the EEG trials are first aligned on the SPD manifold. Then the features are extracted from both the symmetric positive definite (SPD) manifold and Grassmann manifold. Finally, the classification model is learned by combining the structural risk minimization (SRM) of source domain and joint distribution alignment of source and target domains. Experimental results on two MI EEG datasets verify the effectiveness of the proposed METL. In particular, when there are a small amount of labeled samples in the target domain, METL demonstrated a more accurate and stable classification performance than conventional methods. Compared with several state-of-the-art methods, METL has achieved better classification accuracy, 71.81% and 69.06% in single-to-single (STS), 83.14% and 76.00% in multi-to-single (MTS) transfer tasks, respectively. METL can cope with single source domain or multi-source domains and compared with single-source transfer learning, multi-source transfer learning can improve the performance effectively due to the data expansion. It is effective enough to achieve superior performance for classification of EEG signals. • Not only aligning the marginal distribution, but also the conditional distribution. • Operating the form of vector features in the manifold space to reduce time cost. • Using the structural risk minimization to avoid the over-learning problem. [ABSTRACT FROM AUTHOR]