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The existed methods for electroencephalograph (EEG) emotion recognition always train the models based on all the EEG samples indistinguishably. However, some of the source (training) samples may lead to a negative influence because they are significant dissimilar with the target (test) samples. So it is necessary to give more attention to the EEG samples with strong transferability rather than forcefully training a classification model by all the samples. Furthermore, for an EEG sample, from the aspect of neuroscience, not all the brain regions of an EEG sample contains emotional information that can transferred to the test data effectively. Even some brain region data will make strong negative effect for learning the emotional classification model. Considering these two issues, in this paper, we propose a transferable attention neural network (TANN) for EEG emotion recognition, which learns the emotional discriminative information by highlighting the transferable EEG brain regions data and samples adaptively through local and global attention mechanism. This can be implemented by measuring the outputs of multiple brain-region-level discriminators and one single sample-level discriminator. We conduct the extensive experiments on three public EEG emotional datasets. The results validate that the proposed model achieves the state-of-the-art performance.