Emotion recognition is a central and rapidly developing topic in affective intelligence and human-computer interaction. Emotion recognition using electroencephalogram (EEG) signals has attracted considerable attention. However, most existing methods focus only on either time-domain or frequency-domain information, and therefore fail to fully explore the intrinsic correlations and complementary information among multi-domain EEG features. To address this issue, this study proposes an emotion recognition method based on multi-domain feature extraction and staged fusion. First, persistent homology features, differential entropy features, and wavelet brain network features are extracted from the raw EEG signals to comprehensively capture emotion-related information in different dimensions. Then, a multi-branch fusion network, MB-FusionNet, is designed to process each feature type in a targeted manner and perform staged fusion, thus achieving the three-class emotion recognition task. The proposed method is experimentally verified on the SEED dataset, achieving average accuracies of 97.57% and 80.61% for subject-dependent and subject-independent scenarios, respectively. It outperforms comparative algorithms such as BF-GCN in key metrics such as accuracy, demonstrating the superiority and practicality of the proposed method and providing new technical ideas and theoretical support for EEG emotion recognition.