The integral role of sleep in cognition, such as night-time sleep and napping duration, has yielded mixed findings, especially in healthy elderly adults. This study aimed to identify the heterogeneous classes of the cognitive trajectories and investigated the associations between sleep parameters and the trajectories of cognition in different elderly subpopulations. The study was based on a large, national representative sample aged 60 years or older. Two cognitive measures were assessed, including executive function and episodic memory. Sleep parameters were evaluated, including post-lunch napping, night-time sleep duration, and sleep disturbances. Latent growth mixture model (LGMM) was used to describe the trajectories of cognition and investigate the effects of sleep factors on cognition. Three heterogeneous trajectories were identified for executive cognition and four for episodic memory. Inverted U-shape associations of cognition with night-time sleep and napping duration were found. In LGMM, night-time sleep duration was negatively associated with the baseline episodic memory in elderly adults. Post-lunch napping was positively associated with the baseline executive function (β = 0.078, P<0.05) and episodic memory (β = 0.084, P<0.05) in men, whereas it was only associated with impaired episodic memory (β = -0.152, P<0.05) in women. Frequent sleep disturbances were only associated with the impaired executive function at baseline (β = -0.088, 95%CI -0.162, -0.013) among older men. Overall, sleep parameters played different roles in heterogeneous trajectories of cognition by sex difference. Sleep factors may not be related to the rate of cognition decline, but these factors, independent of time-variant depressive symptoms, were associated with the initial status of cognition at baseline.