Creativity is commonly defined as the ability to simultaneously produce novel (original, unique) and useful work within a social context. Social creativity, as a new domain of creativity, is observed when one proposes and solves social problem in the original, appropriate and effective ways. Creativity can be studied from the perspective of state and trait, as many psychologists have studied the psychological variables such as anxiety and self-esteem. With the fast development of neuroscience, research on the brain mechanism of creativity has recently attracted great attention in psychology. Most EEG studies about creativity focused on the alpha activity in the process of creative idea generation. In current study we examined brain mechanisms of social creativity from the perspective of state and trait by recording the EEG of 38 college participants in the social problem scene. We measured participants’ state social creativity using the Questionnaire of Social Creativity for College Students and their trait social creativity using open-ended questionnaire of social problems. The repeated measures ANOVA design in the lower and upper alpha frequency band was used, with state social creativity (high vs. low), hemisphere (left vs. right), and area (prefrontal, frontal, central, parietal, temporal, occipital) as the within-subject factors, and with trait social creativity (high vs. low) as between-subject factor. We found the alpha synchronization in the process of creative social problem solving. A significant main effect of state social creativity was observed on the upper alpha band and the lower alpha band, suggesting that high state social creativity showed a lower alpha synchronization as compared with the low state social creativity. The main effect of hemisphere, area, and the level of trait social creativity failed to reach statistical significance. Moreover, there was the interaction of trait creativity with state creativity, and when presenting high state social creativity, individuals of high trait social creativity showed higher alpha synchronization than their counterparts. However, when they presented low state social creativity, no significant difference was found in alpha synchronization between individuals of high trait social creativity and their counterparts. Furthermore, the interaction between state social creativity and trait social creativity was moderated by the hemisphere. For individuals of low trait social creativity, when manifesting high state social creativity, the alpha synchronization on the right hemisphere was stronger than that on the left hemisphere. However, when manifesting low state social creativity, no significant difference was found between right hemisphere and left hemisphere. For those with high trait social creativity, whenever they presented high or low state social creativity, no significant difference in upper frequency band alpha synchronization was found between left hemisphere and right hemisphere. Similarly, with regard to the lower alpha band, the main effects of state social creativity and the interaction between the state social and trait social creativity were observed, while main effects of other factors failed to reach statistical significance. The simple effect analysis of the interaction indicated the same result as the upper band alpha. Besides, we failed to find the main effect of the brain areas or their interactions with other variables. For future studies, we recommend applying time-course analysis (Schwab, Benedek, Papousek, Weiss, & Fink, 2014) for classifying the cognitive phrases during participants’ creative social problem solving while investigating their EEG. Moreover, we recommend applying longitudinal designs and neuroimaging techniques, such as fMRI and NIR, to explore the brain mechanisms of social creativity from the perspective of trait and state.