Decreased cortical thickness that signifies gray matter pathology and its impact on cognitive performance is a research field with growing interest in relapsing-remitting multiple sclerosis (RRMS) and needs to be further elucidated. Using high-field 3.0 T MRI, three-dimensional T1-FSPGR (voxel size 1 × 1 × 1 mm) cortical thickness was measured in 82 regions in the left hemisphere (LH) and right hemisphere (RH) in 20 RRMS patients with low disease activity and in 20 age-matched healthy subjects that in parallel underwent comprehensive cognitive evaluation. The correlation between local cortical atrophy and cognitive performance was examined. We identified seven regions with cortical tissue loss that differed between RRMS and age-matched healthy controls. These regions were mainly located in the frontal and temporal lobes, specifically within the gyrus rectus, inferior frontal sulcus, orbital gyrus, parahippocampal gyrus, and superior temporal gyrus, with preferential left asymmetry. Increased cortical thickness was identified in two visual sensory regions, the LH inferior occipital gyrus, and the RH cuneus, implicating adaptive plasticity. Correlation analysis demonstrated that only the LH superior temporal gyrus thickness was associated with cognitive performance and its thickness correlated with motor skills (r = 0.65, p = 0.003), attention (r = 0.45, p = 0.042), and information processing speed (r = 0.50, p = 0.025). Our findings show that restricted cortical thinning occurs in RRMS patients with mild disease and that LH superior temporal gyrus atrophy is associated with cognitive dysfunction.