Cortical thinning is a widely used and powerful biomarker for measuring disease progression in Alzheimer's disease (AD). However, there has been little work on the effect of atrophy on the cortical folding patterns. In this study, we examined whether the cortical folding could be used as a biomarker of AD. Cortical folding metrics were computed on 678 patients from the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort. For each subject, the boundary between grey matter and white matter was extracted using a level set technique. At each point on the boundary two metrics characterising folding, curvedness and shape index, were generated. Joint histograms using these metrics were calculated for five regions of interest (ROIs): frontal, temporal, occipital, and parietal lobes as well as the cingulum. Pixelwise statistical maps were generated from the joint histograms using permutations tests. In each ROI, a significant reduction was observed between controls and AD in areas associated with the sulcal folds, suggesting a sulcal opening associated with neurodegeneration. When comparing to MCI patients, the regions of significance were smaller but overlapping with those regions found comparing controls to AD. It indicates that the differences in cortical folding are progressive and can be detected before formal diagnosis of AD. Our preliminary analysis showed a viable signal in the cortical folding patterns for Alzheimer's disease that should be explored further.