Cortical thickness estimation performed in vivo via magnetic resonance imaging (MRI) is an important technique for the diagnosis and understanding of the progression of Alzheimer's disease (AD). Directly using raw cortical thickness measures as features with Support Vector Machine (SVM) for clinical group classification only yields modest results since brain areas are not equally atrophied during AD progression. Therefore, feature reduction is generally required to retain only the most relevant features for the final classification. In this paper, a spherical sparse coding and dictionary learning method is proposed and it achieves relatively high classification results on publicly available data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) 2 dataset (N = 201) which contains structural MRI data of four clinical groups: cognitive unimpaired (CU), early mild cognitive impairment (EMCI), later MCI (LMCI) and AD. The proposed framework takes the estimated cortical thickness and the spherical parameterization computed by FreeSurfer as inputs and constructs weighted patches in the spherical parameter domain of the cortical surface. Then sparse coding is applied to the resulting surface patch features, followed by max-pooling to extract the final feature sets. Finally, SVM is employed for binary group classifications. The results show the superiority of the proposed method over other cortical morphometry systems and offer a different way to study the early identification and prevention of AD.