Background: Depression comprises common psychological problems, and has been strongly related to neuroticism and perceived stress. While neuroticism has been shown to have a direct effect on depression, it also has an indirect effect via perceived stress. Among the elderly, cognitive function produces influences that should not be overlooked when investigating depression. This study aimed to determine the role of mediating effects of perceived stress as well as cognitive function on neuroticism and depression among elderly patients. Methods: This research constituted a secondary analysis, with data collected during the pre-operative period of 429 elderly individuals undergoing elective, noncardiac surgery. The evaluation included the Perceived Stress Scale, the Neuroticism Inventory, the Montreal Cognitive Assessment, and the Geriatric Depression Scale. Structural equation modeling was used to investigate the hypothesized model. Results: Neuroticism exhibited a significant indirect effect on perceived stress via depression and cognition (β = 0.162, 95% CI 0.026, 0.322, p = .002). Neuroticism initially had a direct effect on depression (β = 0.766, 95% CI 0.675, 0.843 p = 0.003); thereafter, it was reduced after covariates were added (β = 0.557, 95% CI 0.432, 0.668 p = 0.002). Based on this model, the total variance explained by this model was 67%, and the model showed an acceptable fit with the data. Conclusions: Both perceived stress and cognitive function partially mediated the effect of neuroticism on depression, with perceived stress exhibiting a greater effect. Trial registration: The study protocol has been registered at Clinicaltrials.gov under registered number: NCT02131181.