The purpose of this study was to investigate the relationship between cognitive function and depressive symptoms among Chinese adults aged 40 years and above, as well as the series of multiple mediating effects of Instrument Activities of Daily Living disability and life satisfaction on this relationship. The data was obtained from the China Health and Retirement Longitudinal Study (CHARLS, 2013–2018), including 6466 adults aged 40 years and above. The mean age of the adults was 57.7 ± 8.5. The SPSS PROCESS macro program was conducted to examine the mediating effects. The results indicated that there was a significant association between cognitive function and depressive symptoms five years later (B = −0.1500, 95%CI: −0.1839, −0.1161), which could also be demonstrated through three mediation pathways: (1) the mediating pathway through IADL disability (B = −0.0247, 95%CI: −0.0332, −0.0171); (2) the mediating pathway through life satisfaction (B = 0.0046, 95%CI: 0.0000, 0.0094); and (3) the chain mediation pathway through IADL disability and life satisfaction (B = −0.0012, 95%CI: −0.0020, −0.0003). Both IADL disability and life satisfaction have been proven to be crucial mediators for the relationship between cognitive function and depressive symptoms five years later. It is necessary to improve individuals’ cognitive function and reduce the negative impact of disability on them, which is important to enhance their life satisfaction and prevent depressive symptoms.