The gated recurrent unit (GRU) network can effectively capture temporal information for 1D signals, such as electroencephalography and event-related brain potential, and it has been widely used in the field of EEG emotion recognition. However, multi-domain features, including the spatial, frequency, and temporal features of EEG signals, contribute to emotion recognition, while GRUs show some limitations in capturing frequency–spatial features. Thus, we proposed a hybrid architecture of convolutional neural networks and GRUs (CGRU) to effectively capture the complementary temporal features and spatial–frequency features hidden in signal channels. In addition, to investigate the interactions among different brain regions during emotional information processing, we considered the functional connectivity relationship of the brain by introducing a phase-locking value to calculate the phase difference between the EEG channels to gain spatial information based on functional connectivity. Then, in the classification module, we incorporated attention constraints to address the issue of the uneven recognition contribution of EEG signal features. Finally, we conducted experiments on the DEAP and DREAMER databases. The results demonstrated that our model outperforms the other models with remarkable recognition accuracy of 99.51%, 99.60%, and 99.59% (58.67%, 65.74%, and 67.05%) on DEAP and 98.63%, 98.7%, and 98.71% (75.65%, 75.89%, and 71.71%) on DREAMER in a subject-dependent experiment (subject-independent experiment) for arousal, valence, and dominance.