Objective Electroencephalogram (EEG) analysis has always been an important tool in neural engineering, and the recognition and classification of human emotions are one of the important tasks in neural engineering. EEG data, obtained from electrodes placed on the scalp, represent a valuable resource of information for brain activity analysis and emotion recognition. Feature extraction methods have shown promising results, but recent trends have shifted toward end-to-end methods based on deep learning. However, these approaches often overlook channel representations, and their complex structures pose certain challenges to model fitting. Approach To address these challenges, this paper proposes a hybrid approach named FetchEEG that combines feature extraction and temporal-channel joint attention. Leveraging the advantages of both traditional feature extraction and deep learning, the FetchEEG adopts a multi-head self-attention mechanism to extract representations between different time moments and channels simultaneously. The joint representations are then concatenated and classified using fully-connected layers for emotion recognition. The performance of the FetchEEG is verified by comparison experiments on a self-developed dataset and two public datasets. Results In both subject-dependent and subject-independent experiments, the FetchEEG demonstrates better performance and stronger generalization ability than the state-of-the-art methods on all datasets. Moreover, the performance of the FetchEEG is analyzed for different sliding window sizes and overlap rates in the feature extraction module. The sensitivity of emotion recognition is investigated for three- and five-frequency-band scenarios. Finally, we perform visualization of the channel-attention to project the model's reliance on different channels onto scalp topographic maps. Significance FetchEEG is a novel hybrid method based on EEG for emotion classification, which significantly improves the performance of recognition and is effective and feasible.