Disruption of the circadian rhythm and sleep–wake cycles is a consequence of aging and is associated with the cognitive decline and many neurodegenerative conditions. We investigated the bedtime, wake-up time, sleep timing (midpoint between bedtime and wake-up time), and sleep timing standard deviation (SD) using the actigraphy among 80 consecutive volunteers aged ≥ 60 years. Global cognitive function and executive function of detailed cognitive domains were evaluated using the mini-mental state examination (MMSE) and Wisconsin card sorting test (WCST) and subjective daytime sleepiness was assessed using the Epworth Sleepiness Scale (ESS). The category achievement (CA), total errors (TE), perseverative errors of Nelson (PEN), non-perseverative errors (NPE), and difficulties in maintaining set (DMS) on the WCST were significantly correlated with sleep timing SD (CA: r = − 0.276, p = 0.013, TE: r = 0.311, p = 0.005, PEN: r = 0.241, p = 0.032, NPE: r = 0.250, p = 0.025, DMS: r = 0.235, p = 0.036), but not with the MMSE score. Multiple regression analyses with the stepwise forward selection method including age, ESS score, bedtime, sleep timing, and sleep timing SD, revealed that the ESS score, and sleep timing SD were significant factors related to CA on the WCST (ESS score: β = − 0.322, p = 0.004; sleep timing SD: β = − 0.250, p = 0.022). Assessment of sleep–wake rhythms, daytime sleepiness, and cognitive function using the MMSE and WCST is valuable for the prediction of cognitive decline in the geriatric population.