Measuring the morphology of brain sulci has been recently proposed as a novel imaging approach in Alzheimer's disease (AD). We aimed to investigate the relevance of such an approach in AD, by exploring its (1) clinical relevance in comparison with traditional imaging methods, (2) relationship with amyloid deposition, (3) association with cognitive functions. Here, 51 patients (n = 32 mild cognitive impairment/mild dementia-AD, n = 19 moderate/severe dementia-AD) diagnosed according to clinical-biological criteria (CSF biomarkers and amyloid-PET) and 29 controls (with negative amyloid-PET) underwent neuropsychological and 3T-MRI examinations. Mean sulcal width (SW) and mean cortical thickness around the sulcus (CT-S) were automatically measured. We found higher SW and lower CT-S in patients with AD than in controls. These differences were more pronounced at later stages of the disease and provided the best diagnostic accuracies among the imaging markers. Correlations were not found between CT-S or SW and amyloid deposition but between specific cognitive functions and regional CT-S/SW in key associated regions. Sulcal morphology is a good supporting diagnosis tool that reflects the main cognitive impairments in AD. It could be considered as a good surrogate marker to evaluate the efficacy of new drugs. •Examination of sulcal morphology alterations is a good diagnosis tool for Alzheimer's disease.•This imaging marker is more accurate than traditional imaging tools such as hippocampal volume.•Sulcal morphology alterations are correlated to specific cognitive impairment observed.•Sulcal morphology alterations are related to disease severity.