Most previous EEG-based emotion recognition methods studied hand-crafted EEG features extracted from different electrodes. In this paper, we study the relation among different EEG electrodes and propose a deep learning method to automatically extract the spatial features that characterize the functional relation between EEG signals at different electrodes. Our proposed deep model is called ATtention-based LSTM with Domain Discriminator (ATDD-LSTM) that can characterize nonlinear relations among EEG signals of different electrodes. To achieve state-of-the-art emotion recognition performance, the architecture of ATDD-LSTM has two distinguishing characteristics: (1) By applying the attention mechanism to the feature vectors produced by LSTM, ATDD-LSTM automatically selects suitable EEG channels for emotion recognition, which makes the learned model concentrate on the emotion related channels in response to a given emotion; (2) To minimize the significant feature distribution shift between different sessions and/or subjects, ATDD-LSTM uses a domain discriminator to modify the data representation space and generate domain-invariant features. We evaluate the proposed ATDD-LSTM model on three public EEG emotional databases (DEAP, SEED and CMEED) for emotion recognition. The experimental results demonstrate that our ATDD-LSTM model achieves superior performance on subject-dependent (for the same subject), subject-independent (for different subjects) and cross-session (for the same subject) evaluation.