The relationship between cognitive functions and brain structure has been of long-standing research interest. Most previous research has attempted to relate cognition to volumes of specific brain structures or thickness of cortical regions, with relatively few studies examining other features such as cortical surface anatomy. In this study, we examine the relationship between cortical sulcal features and cognitive function in a sample (N = 316) of community-dwelling subjects aged between 70 and 90 years (mean = 78.06 ± 4.75; male/female = 130/186) who had detailed neuropsychological assessments and brain MRI scans. Using automated methods on 3D T1-weighted brain scans, we computed global sulcal indices (g-SIs) of the whole brain and average sulcal spans of five prominent sulci. The g-SI, which reflects the complexity of sulcal folds across the cerebral hemispheres, showed a significant positive correlation with performance in most cognitive domains including attention/processing speed, memory, language and executive function. Regionally, a negative correlation was found between some cognitive functions and sulcal spans, i.e. poorer cognitive performance was associated with a wider sulcal span. Of the five cognitive domains examined, the performance of processing speed was found to be correlated with the spans of most sulci, with the strongest correlation being with the superior temporal sulcus. Memory did not show a significant correlation with any individual sulcal index, after correcting for age and sex. Of the five sulci measured, the left superior temporal sulcus showed the highest sensitivity, with significant correlations with performances in all cognitive domains except memory, after controlling for age, sex, years of education and brain size. The results suggest that regionally specific sulcal morphology is associated with cognitive function in elderly individuals.