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The Internet holds potential for alleviating cognitive decline through cognitive stimulation and social engagement. However, existing studies often overlook the crucial role of Internet access as the foundational layer of the digital divide. This study investigated the association between Internet access and cognitive function among middle-aged and older adults and examined age-specific differences in this relationship. Data were drawn from the 2015 and 2018 waves of the China Health and Retirement Longitudinal Study (CHARLS). Participants aged ≥ 50 years with complete follow-up cognitive assessments were included (n = 7721; mean age = 60.48, SD = 9.37; male, 56.1%). Lagged dependent variable models were used to evaluate associations between Internet access and cognitive function. Chain mediation analyses were used to test whether family connection mediated this association. Internet access was significantly associated with better cognitive outcomes over time. Participants with Internet access demonstrated greater significant improvements in episodic memory (β = 0.29,95%CI = 0.14-0.44) and mental status (β = 0.28,95%CI = 0.12-0.44) compared to those without access. Age-stratified models indicated stronger effects in adults aged 50-59 for episodic memory (β = 0.36,95%CI = 0.17-0.55) and aged 60-69 for mental status (β = 0.42,95%CI = 0.15-0.69). Chain mediation analyses revealed that Internet access enhanced family connection, thereby contributing to better cognitive function. Internet access is positively associated with cognitive function in mid- to later life, partly through strengthened family ties. These findings underscore the importance of digital inclusion policies to support cognitive health and promote healthy aging.