Electroencephalograph (EEG) emotion recognition is a significant task in the brain-computer interface field. Although many deep learning methods are proposed recently, it is still challenging to make full use of the information contained in different domains of EEG signals. In this paper, we present a novel method, called four-dimensional attention-based neural network (4D-aNN) for EEG emotion recognition. First, raw EEG signals are transformed into 4D spatial-spectral-temporal representations. Then, the proposed 4D-aNN adopts spectral and spatial attention mechanisms to adaptively assign the weights of different brain regions and frequency bands, and a convolutional neural network (CNN) is utilized to deal with the spectral and spatial information of the 4D representations. Moreover, a temporal attention mechanism is integrated into a bidirectional Long Short-Term Memory (LSTM) to explore temporal dependencies of the 4D representations. Our model achieves state-of-the-art performances on both DEAP, SEED and SEED-IV datasets under intra-subject splitting. The experimental results have shown the effectiveness of the attention mechanisms in different domains for EEG emotion recognition.