Abstract Background Cognitive impairment, a common and debilitating symptom in people with multiple sclerosis (MS), is especially related to cortical damage. However, the impact of regional cortical damage remains poorly understood. Our aim was to evaluate structural (network) integrity in lesional and non-lesional cortex in people with MS, and its relationship with cognitive dysfunction. Methods In this cross-sectional study, 176 people with MS and 48 healthy controls underwent MRI, including double inversion recovery and diffusion-weighted scans, and neuropsychological assessment. Cortical integrity was assessed based on fractional anisotropy (FA) and mean diffusivity (MD) within 212 regions split into lesional or non-lesional cortex, and grouped into seven cortical networks. Integrity was compared between people with MS and controls, and across cognitive groups: cognitively-impaired (CI; ≥ two domains at Z ≤ − 2 below controls), mildly CI (≥ two at − 2 < Z ≤ − 1.5), or cognitively-preserved (CP). Results Cortical lesions were observed in 87.5% of people with MS, mainly in ventral attention network, followed by limbic and default mode networks. Compared to controls, in non-lesional cortex, MD was increased in people with MS, but mean FA did not differ. Within the same individual, MD and FA were increased in lesional compared to non-lesional cortex. CI-MS exhibited higher MD than CP-MS in non-lesional cortex of default mode, frontoparietal and sensorimotor networks, of which the default mode network could best explain cognitive performance. Conclusion Diffusion differences in lesional cortex were more severe than in non-lesional cortex. However, while most people with MS had cortical lesions, diffusion differences in CI-MS were more prominent in non-lesional cortex than lesional cortex, especially within default mode, frontoparietal and sensorimotor networks.