Voxel-based morphometry provides an opportunity to study Alzheimer’s disease (AD) at a subtle level. Therefore, identifying the important brain voxels that can classify AD, early mild cognitive impairment (EMCI) and healthy control (HC) and studying the role of these voxels in AD will be crucial to improve our understanding of the neurobiological mechanism of AD. Combining magnetic resonance imaging (MRI) imaging and gene information, we proposed a novel feature construction method and a novel genetic multi-kernel support vector machine (SVM) method to mine important features for AD detection. Specifically, to amplify the differences among AD, EMCI and HC groups, we used the eigenvalues of the top 24 Single Nucleotide Polymorphisms (SNPs) in a p-value matrix of 24 genes associated with AD for feature construction. Furthermore, a genetic multi-kernel SVM was established with the resulting features. The genetic algorithm was used to detect the optimal weights of 3 kernels and the multi-kernel SVM was used after training to explore the significant features. By analyzing the significance of the features, we identified some brain regions affected by AD, such as the right superior frontal gyrus, right inferior temporal gyrus and right superior temporal gyrus. The findings proved the good performance and generalization of the proposed model. Particularly, significant susceptibility genes associated with AD were identified, such as CSMD1, RBFOX1, PTPRD, CDH13 and WWOX. Some significant pathways were further explored, such as the calcium signaling pathway (corrected p-value = 1.35 × 10−6) and cell adhesion molecules (corrected p-value = 5.44 × 10−4). The findings offer new candidate abnormal brain features and demonstrate the contribution of these features to AD.