Accurate identification and understanding informative feature is important for early Alzheimer's disease (AD) prognosis and diagnosis. In this paper, we propose a novel discriminative sparse learning method with relational regularization to jointly predict the clinical score and classify AD disease stages using multimodal features. Specifically, we apply a discriminative learning technique to expand the class-specific difference and include geometric information for effective feature selection. In addition, two kind of relational information are incorporated to explore the intrinsic relationships among features and training subjects in terms of similarity learning. We map the original feature into the target space to identify the informative and predictive features by sparse learning technique. A unique loss function is designed to include both discriminative learning and relational regularization methods. Experimental results based on a total of 805 subjects [including 226 AD patients, 393 mild cognitive impairment (MCI) subjects, and 186 normal controls (NCs)] from AD neuroimaging initiative database show that the proposed method can obtain a classification accuracy of 94.68% for AD versus NC, 80.32% for MCI versus NC, and 74.58% for progressive MCI versus stable MCI, respectively. In addition, we achieve remarkable performance for the clinical scores prediction and classification label identification, which has efficacy for AD disease diagnosis and prognosis. The algorithm comparison demonstrates the effectiveness of the introduced learning techniques and superiority over the state-of-the-arts methods.