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Alzheimer’s disease (AD) is a progressive dementia in which the brain shrinks as the disease progresses. The use of machine learning and brain magnetic resonance imaging (MRI) for the early diagnosis of AD has a high probability of clinical value and social significance. Sparse representation classifier (SRC) is widely used in MRI image classification. However, the traditional SRC only considers the reconstruction error and classification error of the dictionary, and does not consider the global and local structural information between images, which results in unsatisfactory classification performance. Therefore, a large margin and local structure preservation sparse representation classifier (LMLS-SRC) is developed in this manuscript. The LMLS-SRC algorithm uses the classification large margin term based on the representation coefficient, which results in compactness between representation coefficients of the same class and a large margin between representation coefficients of different classes. The LMLS-SRC algorithm uses local structure preservation term to inherit the manifold structure of the original data. In addition, the LMLS-SRC algorithm imposes the ℓ2,1-norm on the representation coefficients to enhance the sparsity and robustness of the model. Experiments on the KAGGLE Alzheimer’s dataset show that the LMLS-SRC algorithm can effectively diagnose non AD, moderate AD, mild AD, and very mild AD.