Hemispheric lateralization is linked to potential cognitive advantages. It is considered a driving force behind the generation of human intelligence. However, establishing quantitative links between the degree of lateralization and intelligence in humans remains elusive. In this study, we propose a framework that utilizes the functional aligned multidimensional representation space derived from hemispheric functional gradients to compute between-hemisphere distances within this space. Applying this framework to a large cohort (N = 777), we identified high functional divergence across the two hemispheres within the frontoparietal network. We found that both global divergence between the cerebral hemispheres and regional divergence within the multiple demand network were positively associated with fluid composite score and partially mediated the relationship between brain size and individual differences in fluid intelligence. Together, these findings deepen our understanding of hemispheric lateralization as a fundamental organizational principle of the human brain, providing empirical evidence for its role in supporting fluid intelligence.