Fluid intelligence (Gf) is the innate ability of an individual to respond to complex and unexpected situations. Although some studies have considered that the multiple-demand (MD) system of the brain was the biological foundation for Gf, further characterization of their relationships in the context of aging is limited. The present study hypothesized that the structural metrics of the MD system, including cortical thickness, cortical volumes, and white matter (WM) tract integrity, was the brain correlates for Gf across the adult life span. Partial correlation analysis was performed to investigate whether the MD system could still explain Gf independent of the age effect. Moreover, the partial correlations between Gf and left/right structural metrics within the MD regions were compared to test whether the correlations displayed distinct lateralization. The participants were recruited from the Cambridge Centre for Ageing and Neuroscience (Cam-CAN) databank, comprising the images of 603 healthy participants aged 18-88 years acquired on a 3-T system. The MRI data included high-resolution T1-weighted and diffusion-weighted images, from which gray matter and WM structural metrics of the MD system were analyzed, respectively. The structural metrics of gray matter were quantified in terms of cortical volume/thickness of five pairs of cortical regions, and those of WM were quantified in terms of the mean axial diffusivity (DA), radial diffusivity (DR), mean diffusivity (DM), and generalized fractional anisotropy (GFA) on five pairs of tracts. Partial correlation controlling for age and sex effects, was performed to investigate the associations of Gf scores with the mean DA, DR, DM and GFA of all tracts in the MD system, those of left and right hemispheric tracts, and those of each tract. Fisher's exact test was used to compare the partial correlations between left and right MD regions. The linear relationship between cortical volumes and Gf was evident across all levels of the MD system even after controlling for age and sex. For the WM integrity, diffusion indices including DA, DR, DM and GFA displayed linear relationships with Gf scores at various levels of the MD system. Among the 10 WM tracts connecting the MD regions, bilateral superior longitudinal fasciculus I and bilateral frontal aslant tracts exhibited the strongest and significant associations. Our results did not show significant inter-hemispheric differences in the associations between structural metrics of the MD system and Gf. Our results demonstrate significant associations between Gf and both cortical volumes and tract integrity of the MD system across the adult lifespan in a population-based cohort. We found that the association remained significant in the entire adult lifespan despite simultaneous decline of Gf and the MD system. Our results suggest that the MD system might be a structural underpinning of Gf and support the fronto-parietal model of cognitive aging. However, we did not find hemispheric differences in the Gf-MD correlations, not supporting the hemi-aging hypothesis.