As the key to realizing aBCIs, EEG emotion recognition has been widely studied by many researchers. Previous methods have performed well for intra-subject EEG emotion recognition. However, the style mismatch between source domain (training data) and target domain (test data) EEG samples caused by huge inter-domain differences is still a critical problem for EEG emotion recognition. To solve the problem of cross-dataset EEG emotion recognition, in this paper, we propose an EEG-based Emotion Style Transfer Network (E2STN) to obtain EEG representations that contain the content information of source domain and the style information of target domain, which is called stylized emotional EEG representations. The representations are helpful for cross-dataset discriminative prediction. Concretely, E2STN consists of three modules, i.e., transfer module, transfer evaluation module, and discriminative prediction module. The transfer module encodes the domain-specific information of source and target domains and then re-constructs the source domain's emotional pattern and the target domain's statistical characteristics into the new stylized EEG representations. In this process, the transfer evaluation module is adopted to constrain the generated representations that can more precisely fuse two kinds of complementary information from source and target domains and avoid distorting. Finally, the generated stylized EEG representations are fed into the discriminative prediction module for final classification. Extensive experiments show that the E2STN can achieve the state-of-the-art performance on cross-dataset EEG emotion recognition tasks.