Structural asymmetries of the human brain have been widely studied in previous research. However, there is a lack of consistency across studies in terms of whether brain regions are larger in the left hemisphere than the right (leftward asymmetry), larger in the right hemisphere than the left (rightward asymmetry), or similar in both hemispheres (no asymmetry). Moreover, some of the existing studies exploring brain asymmetry were based on only small sample sizes and/or restricted to younger participants. Thus, here we analysed brain asymmetry in a well-powered sample (n = 532) later in life (mean age: 67 years). Given that language is known to be strongly lateralized in the brain, the current study focused on regions related to language. When assessing cortical volumes and surface areas, we observed significant leftward asymmetries for the superior temporal gyrus, superior temporal sulcus, supramarginal gyrus, pars opercularis, transverse gyrus, and temporal gyrus, whereas the pars triangularis showed a significant rightward asymmetry. In contrast, when assessing cortical thickness, we detected a significant leftward asymmetry for the pars triangularis and a significant rightward asymmetry for the superior temporal sulcus. The present observations on asymmetry in language-related brain regions in a large sample of older but neurologically healthy participants may serve as a normative framework against which data from clinical samples can be compared.