Hyperscanning is a brain imaging technique that measures brain synchrony caused by social interactions. Recent research on hyperscanning has revealed substantial inter-brain synchrony (IBS), but little is known about the link between IBS and mental workload. To study this link, we conducted an experiment consisting of button-pressing tasks of three different difficulty levels for the cooperation and competition modes with 56 participants aged 23.7± 3.8 years (mean±standard deviation). We attempted to observe IBS using functional near-infrared spectroscopy (fNIRS) and galvanic skin response (GSR) to assess the activities of the human autonomic nervous system. We found that the IBS levels increased in a frequency band of 0.075-0.15 Hz, which was unrelated to the task repetition frequency in the cooperation mode according to the task difficulty level. Significant relative inter-brain synchrony (RIBS) increases were observed in three and 10 channels out of 15 for the hard tasks compared to the normal and easy tasks, respectively. We observed that the average GSR values increased with increasing task difficulty levels for the competition mode only. Thus, our results suggest that the IBS revealed by fNIRS and GSR is not related to the hemodynamic changes induced by mental workload, simple behavioral synchrony such as button-pressing timing, or autonomic nervous system activity. IBS is thus explicitly caused by social interactions such as cooperation.