To accurately evaluate individual emotional states， we propose a graph feature learning and recognition algorithm for electroencephalogram（EEG）-based emotion recognition. In the proposed algorithm， the original EEG data are first used to construct the corresponding EEG network. And then， the local adjacency graph between different emotional EEG network samples is constructed in the high-dimensional EEG brain network space， which aims to capture the distribution of the emotional EEG brain networks， and the graph Laplacian matrix can be estimated with the adjacency graph. Thirdly， the optimal low-dimensional graph embeddings of emotional EEG brain networks are obtained by the spectral graph theory， and the emotional EEG brain network samples can be represented in the low-dimensional space， in which the initial emotional EEG brain networks can be represented with a set of network features. Finally， based on the extracted emotional EEG brain network features， the optimal support vector machine classifier is trained and utilized in the emotion recognition. The verification experiment is carried out on the international public emotional EEG datasets， and experimental results show that compared with traditional emotion recognition algorithms， the proposed method can effectively improve the accuracy of emotion recognition， and achieve a robust recognition effect of 91.85% （SEED dataset， 3-class）， 79.36% （MAHNOB-HCI dataset， 3-class） and 79% （DEAP dataset， 4-class） on three public datasets， respectively.