Studies in the area of neuroscience have revealed the relationship between emotional patterns and brain functional regions, demonstrating that dynamic relationships between different brain regions are an essential factor affecting emotion recognition determined through electroencephalography (EEG). Moreover, in EEG emotion recognition, we can observe that clearer boundaries exist between coarse-grained emotions than those between fine-grained emotions, based on the same EEG data; this indicates the concurrence of large coarse- and small fine-grained emotion variations. Thus, the progressive classification process from coarse- to fine-grained categories may be helpful for EEG emotion recognition. Consequently, in this study, we propose a progressive graph convolution network (PGCN) for capturing this inherent characteristic in EEG emotional signals and progressively learning the discriminative EEG features. To fit different EEG patterns, we constructed a dual-graph module to characterize the intrinsic relationship between different EEG channels, containing the dynamic functional connections and static spatial proximity information of brain regions from neuroscience research. Moreover, motivated by the observation of the relationship between coarse- and fine-grained emotions, we adopt a dual-head module that enables the PGCN to progressively learn more discriminative EEG features, from coarse-grained (easy) to fine-grained categories (difficult), referring to the hierarchical characteristic of emotion. To verify the performance of our model, extensive experiments were conducted on two public datasets: SEED-IV and multi-modal physiological emotion database (MPED).