The human brain is a complex network that has been noted to contain a group of densely interconnected hub regions. With a putative “rich club” of hubs hypothesized to play a central role in global integrative brain functioning, we assessed whether hub and rich club organizations are associated with cognitive performance in healthy participants and whether the rich club might be differentially involved in cognitive functions with a heavier dependence on global integration. A group of 30 relatively older participants (range = 39–79 years of age) underwent extensive neuropsychological testing, combined with diffusion-weighted magnetic resonance imaging to reconstruct individual structural brain networks. Rich club connectivity was found to be associated with general cognitive performance. More specifically, assessing the relationship between the rich club and performance in two specific cognitive domains, we found rich club connectivity to be differentially associated with attention/executive functions—known to rely on the integration of distributed brain areas—rather than with visuospatial/visuoperceptual functions, which have a more constrained neuroanatomical substrate. Our findings thus provide first empirical evidence of a relevant role played by the rich club in cognitive processes.