This study evaluated the association between cognition and social capital among Chinese older adults and analyzed the mediating role of functional health in that interaction. The baseline and follow-up data were acquired from the 2011 and 2015 China Health and Retirement Longitudinal Study (CHARLS). The sample included 6291 adults aged 55 years and above in 2011. The dimensions of social capital included social trust, social support, social participation, and reciprocity. Cognition was measured based on mental state and episodic memory. The Karlson-Holm-Breen method was employed to explore the association between social capital at the baseline and cognition four years later, and the mediating role of baseline functional health. There was a positive relationship between financial support (one of the social support variables) and reciprocity, and mental state (β = 0.186, p = 0.00; β = 0.306, p = 0.012). Furthermore, a positive relationship between social participation and episodic memory (β = 0.129, p = 0.002) was observed. The mediating effect of functional health explained 7.7% of the total effect of social participation on episodic memory. These findings may contribute to research concerning the potential explanation of the association between social capital and cognition as well as interventions aimed at improving cognitive performance in older adults.