In recent years, electroencephalogram (EEG) e-motion recognition has been becoming an emerging field in artificial intelligence area, which can reflect the relation between emotional states and brain activity. In this paper, we designed a novel architecture, i.e., broad dynamical graph learning system (BDGLS), to deal with EEG signals. By integrating the advantage of dynamical graph convolution neural networks (DGCNN) and broad learning system (BLS), BDGLS has the ability of extracting features on non-Euclidean domain and randomly generating nodes to find the desired connection weights simultaneously. We evaluated our system on SJTU emotion EEG dataset (SEED), and used differential entropy (DE) features as input data. In the experiments, BDGLS achieved the best result, compared with the state-of-the-art methods, e.g., support vector machine (SVM), deep belief networks (DBN), graph convolutional neural networks (DCNN) and DGCNN. Especially the performance on all-frequency band of DE features, BDGLS reached the highest average recognition accuracy of 93.66% with the standard deviation of 6.11%. The result demonstrated the excellent classification ability of BDGLS in EEG emotion recognition.