In this paper, we consider the joint regression and classification in Alzheimer's disease diagnosis and propose a novel multi-relation regularization method that exploits the relational information inherent in the observations and then combines it with an L2,1-norm within a least square regression framework for feature selection. Specifically, we use three kinds of relationships: feature-feature relation, response-response relation, and sample-sample relation. By imposing these three relational characteristics along with the L2,1-norm on the weight coefficients, we formulate a new objective function. After feature selection based on the optimal weight coefficients, we train two support vector regression models to predict the clinical scores of Alzheimer's Disease Assessment Scale-Cognitive subscale (ADAS-Cog) and Mini-Mental State Examination (MMSE), respectively, and a support vector classification model to identify the clinical label. We conducted clinical score prediction and disease status identification jointly on the Alzheimer's Disease Neuroimaging Initiative dataset. The experimental results showed that the proposed regularization method outperforms the state-of-the-art methods, in the metrics of correlation coefficient and root mean squared error in regression and classification accuracy, sensitivity, specificity, and area under the receiver operating characteristic curve in classification.