In this paper, we applied a novel method for the detection of Alzheimer’s disease (AD) based on a structural magnetic resonance imaging (sMRI) dataset. Specifically, the method involved a new classification algorithm of machine learning, named Generalized Split Linearized Bregman Iteration (GSplit LBI). It combines logistic regression and structural sparsity regularizations. In the study, 57 AD patients and 47 normal controls (NCs) were enrolled. We first extracted the entire brain gray matter volume values of all subjects and then used GSplit LBI to build a predictive classification model with a 10-fold full cross-validation method. The model accuracy achieved 90.44%. To further verify which voxels in the dataset have greater impact on the prediction results, we ranked the weight parameters and obtained the top 6% of the model parameters. To verify the generalization of model prediction and the stability of feature selection, we performed a cross-test on the Alzheimer's Disease Neuroimaging Initiative (ADNI) and a Chinese dataset and achieved good performances on different cohorts. Conclusively, based on the sMRI dataset, our algorithm not only had good performance in a local cohort with high accuracy but also had good generalization of model prediction and stability of feature selection in different cohorts.