Social relationships are widely identified as important predictors of cognitive health. However, this generalization may obscure the multidimensionality of relationships and simplify the dynamics within relationships. The conflation of network characteristics and support/strain prevents us from understanding their relative influences. More importantly, few studies have paid attention to the coexistence of support and strain and examined how they work synergistically to affect cognitive health. Aiming to bridge the gaps in prior literature, this study examines the relationship between network characteristics, relationship quality, and cognitive function with Waves 2 and 3 data from the National Social Life, Health and Aging Project (NSHAP). Drawing on the relationship typology, this study focuses on relationships with partners, families, and friends, and classifies relationship quality as supportive (high support, low strain), aversive (low support, high strain), ambivalent (high support, high strain), and indifferent (low support, low strain). Results from the lagged dependent variable regression models indicate that network characteristics (network size, range, and frequency of contact) do not have an obvious influence on cognitive function. For relationship quality, women in ambivalent and aversive partnerships have worse cognitive functioning than counterparts in supportive partnerships. However, men in ambivalent partnerships may have slightly better cognitive functioning than counterparts in supportive partnerships. Moreover, compared with counterparts with supportive friends, women in aversive friendships have worse cognitive functioning, and men in indifferent friendships have better cognitive functioning. This study highlights the importance of relationship quality for cognitive health and calls for theoretical and empirical discussion on the gender-specific mechanisms linking social relationships and cognitive functioning in later life.