Alzheimer's disease (AD) is a progressive neurodegenerative disease characterized by cerebral cortex atrophy. In this study, we used sparse canonical correlation analysis (SCCA) to identify associations between single nucleotide polymorphisms (SNPs) and cortical thickness in the Korean population. We also investigated the role of the SNPs in neurological outcomes, including neurodegeneration and cognitive dysfunction. We recruited 1125 Korean participants who underwent neuropsychological testing, brain magnetic resonance imaging, positron emission tomography, and microarray genotyping. We performed group-wise SCCA in Aβ negative (-) and Aβ positive (+) groups. In addition, we performed mediation, expression quantitative trait loci, and pathway analyses to determine the functional role of the SNPs. We identified SNPs related to cortical thickness using SCCA in Aβ negative and positive groups and identified SNPs that improve the prediction performance of cognitive impairments. Among them, rs9270580 was associated with cortical thickness by mediating Aβ uptake, and three SNPs (rs2271920, rs6859, rs9270580) were associated with the regulation of CHRNA2, NECTIN2, and HLA genes. Our findings suggest that SNPs potentially contribute to cortical thickness in AD, which in turn leads to worse clinical outcomes. Our findings contribute to the understanding of the genetic architecture underlying cortical atrophy and its relationship with AD.