Electroencephalogram (EEG) brain network embodies the brain's coordination and interaction mechanism, and the transformations of emotional states are usually accompanied with changes in brain network spatial topologies. To effectively characterize emotions, in this work, we propose a cognition-inspired graph embedding model in the L1-norm space (L1-CGE) to learn an optimal low-dimensional embedded manifold for emotional brain networks. In the L1-CGE, the original brain networks are first encoded in the affinity space with the proposed cognition-inspired metric to construct the latent geometry manifold structure of emotional brain networks, and then the graph learning objective function is defined in the L1-norm space to obtain the optimal low-dimensional representations of brain networks. Essentially, the modularized community structures of emotional brain networks can be effectively emphasized by the L1-CGE to realize an effective depiction for emotions. Compared with existing methods, the L1-CGE model has achieved state-of-the-art performance on three public emotional EEG datasets in off-line conditions. Besides, the robust real-time experimental results have been achieved with the on-line emotion decoding system designed with L1-CGE. Both off-and on-line experimental results consistently demonstrate that the proposed L1-CGE is promising to provide a potential solution for the real-time affective brain-computer interface (aBCI) system.