Previous studies on insight problem solving using Chinese logogriphs as insight problems only investigated the time- and phase-locked changes of electrocortical responses triggered by Chinese logogriphs, but did not focus on what kind of brain state facilitates individuals to solve insight problems. To investigate this, we focused on participants’ alpha activities (8–12 Hz) that closely correlates with insight problem solving and defocused attention while they were solving Chinese logogriphs. Results indicated that in the time window of 800–1400 ms after the presentation of target logogriphs, alpha power over parieto-central electrodes decreased relative to the reference interval in both the successful and unsuccessful logogriphs solving conditions. However, alpha power increased at parieto-occipital electrode sites in successful conditions compared with that in unsuccessful condition. The decrease in alpha activity in both conditions may reflect the cognitive demands in solving the target logogriphs. Furthermore, difference in alpha power between the successful and unsuccessful conditions at parieto-occipital electrode sites is associated with the process of heuristic information. Alpha synchronization observed in the successful condition compared to the unsuccessful condition might reflect a state of defocused attention that facilitates insight problem solving.