In the design process, different problem statements result in different problem-solving strategies. A proper problem statement is the key to effective problem-solving. Based on the characteristics of the product design process, we divided design problem statements into open-ended (OE), decision-making (DM), and constrained (CO) statements and attempted to investigate the influences of different problem statements on designers’ cognitive behaviors from three perspectives, namely divergent thinking, convergent thinking, and mental workload. Then we provided quantification description to these influences based on electroencephalography (EEG) technology. We conducted experiments on 19 participants and used the BrainProduct™ actiChamp-32 to record the EEG data. Results are as follows: (1) The higher task-related α power was found in the temporal and occipital regions in the OE task compared with that in the DM and CO tasks. The OE statement also would help designers get novel ideas by strengthening their divergent thinking. (2) In the DM and CO tasks, there was no significant difference in the impact of the brain region on convergent thinking, but activities in the left hemisphere were stronger than that in the right hemisphere. The DM and CO tasks have better performance in convergent thinking than the OE task. (3) In the CO task, the designer's mental workload is the highest and mainly related to the activation of the centroparietal and occipital regions. These findings help designers understand the design problem-solving process from the perspective of cognitive science and monitor their thinking modes in the design process so as to improve their design performance.