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Objective This study aimed to investigate the associations between loneliness and its components and cognitive function among older Chinese adults living in nursing homes and to test whether depressive symptoms, anxiety symptoms, and sleep disturbances mediate these associations. Methods The sample comprised 228 Chinese individuals aged ≥ 65 years living in nursing homes who were free of dementia and psychiatric or serious somatic diseases. Loneliness was evaluated using the UCLA Loneliness Scale. Global cognitive function was assessed using the Beijing version of the Montreal Cognitive Assessment. Multivariable linear regression analyses were performed to examine the associations between loneliness and its components and global cognitive function. A mediation analysis was used to test the potential mediating effects of depressive symptoms, anxiety symptoms, and sleep disturbances. Results The mean (SD) age of the participants was 80.8 (6.3) years, and 58.3% were women. Compared with the lowest quartile of loneliness degree, the multivariable-adjusted beta coefficient (95% confidence interval [95% CI]) for the highest quartile was -1.32 (-2.61 to -0.02) (P for trend = 0.03). Loneliness components, personal feelings of isolation and the lack of relational connectedness but not the lack of collective connectedness, were also inversely associated with cognitive function. Significant indirect effects on cognitive function were observed for loneliness and its two components (personal feelings of isolation and the lack of relational connectedness) in mediating pathways via depressive symptoms, anxiety symptoms, and sleep disturbances (all p < 0.05). Conclusions A higher degree of loneliness and its two components, personal feelings of isolation and the lack of relational connectedness, are associated with worse cognitive function among Chinese residents in nursing homes. Depressive symptoms, anxiety symptoms, and sleep disturbances may at least partially mediate these associations.