Eye movement patterns are found to reveal human cognitive and mental states that can not be easily measured by other biological signals. With the rapid development of eye tracking technologies, there are growing interests in analysing gaze data to infer information about people’ cognitive states, tasks and activities performed in naturalistic environments. In this paper, we investigate the link between eye movements and cognitive function. We conducted experiments to record subject’s eye movements during video watching. By using computational methods, we identified eye movement features that are correlated to people’s cognitive health measures obtained through the standard cognitive tests. Our results show that it is possible to infer people’s cognitive function by analysing natural gaze behaviour. This work contributes an initial understanding of monitoring cognitive deterioration and dementia with automatic eye movement analysis.