We investigated the association between individual differences in cognitive performance in old age and the approximate entropy (ApEn) measured from functional magnetic resonance imaging (fMRI) data acquired from 40 participants of the Aberdeen Birth Cohort 1936 (ABC1936), while undergoing a visual information processing task: inspection time (IT). Participants took a version of the Moray House Test (MHT) No. 12 at age 11, a valid measure of childhood intelligence. The same individuals completed a test of non-verbal reasoning (Raven's Standard Progressive Matrices [RPM]) aged about 68 years. The IT, MHT and RPM scores were used as indicators of cognitive performance. Our results show that higher regional signal entropy is associated with better cognitive performance. This finding was independent of ability in childhood but not independent of current cognitive ability. ApEn is used for the first time to identify a potential source of individual differences in cognitive ability using fMRI data.