Affective computing is a key problem in modern human-computer interaction, and with the development of artificial intelligence, emotion recognition based on electroencephalogram (EEG) has become an important research direction. To improve the classification accuracy of emotion recognition, this study introduces stacked auto-encoder (SAE) to extract the deep feature of EEG multichannel signals and then proposes a generalized normal distribution optimization based support vector machine (GNDO-SVM). The experimental results show that the proposed GNDO-SVM model has better classification performance than the support vector machine model optimized by genetic algorithm, particle swarm optimization algorithm, and sparrow search algorithm. The accuracy of emotion recognition based on SAE depth features reaches 90.94%, indicating that SAE can effectively exploit the depth correlation information between different channels of EEG signals. Therefore, applying SAE depth feature extraction combined with the GNDO-SVM classification model can effectively achieve the emotion recognition of EEG signals.