In neuroimaging studies, the human cortex is commonly modelled as a sphere to preserve the topological structure of the cortical surface. In this work, we explore the analysis of the human cortex using spherical CNN in an Alzheimer's disease (AD) classification task, using morphometric measures derived from T1-weighted structural MRI. Our results show superior performance in classifying AD versus cognitively normal subjects and in predicting mild cognitive impairment progression within two years. This work demonstrates the feasibility and superiority of the spherical CNN directly applied on the spherical representation in the discriminative analysis of the human cortex and could be readily extended to other imaging modalities and other neurological diseases.