Alzheimer's disease (AD) is one of the most frequent forms of dementia and an increasing challenging public health problem. In the last two decades, structural magnetic resonance imaging (MRI) has shown potential in distinguishing patients with Alzheimer's disease and elderly controls (CN). To obtain AD-specific biomarkers, previous research used either statistical testing to find statistically significant different regions between the two clinical groups, or ℓ1 sparse learning to select isolated features in the image domain. In this paper, we propose a new framework that uses structural MRI to simultaneously distinguish the two clinical groups and find the bio-markers of AD, using a group lasso support vector machine (SVM). The group lasso term (mixed ℓ1- ℓ2 norm) introduces anatomical information from the image domain into the feature domain, such that the resulting set of selected voxels are more meaningful than the ℓ1 sparse SVM. Because of large inter-structure size variation, we introduce a group specific normalization factor to deal with the structure size bias. Experiments have been performed on a well-designed AD vs. CN dataset1 to validate our method. Comparing to the ℓ1 sparse SVM approach, our method achieved better classification performance and a more meaningful biomarker selection. When we vary the training set, the selected regions by our method were more stable than the ℓ1 sparse SVM. Classification experiments showed that our group normalization lead to higher classification accuracy with fewer selected regions than the non-normalized method. Comparing to the state-of-art AD vs. CN classification methods, our approach not only obtains a high accuracy with the same dataset, but more importantly, we simultaneously find the brain anatomies that are closely related to the disease.