Accurately diagnosing Alzheimer’s disease is essential for improving elderly health. Meanwhile, accurate prediction of the mini-mental state examination score also can measure cognition impairment and track the progression of Alzheimer’s disease. However, most of the existing methods perform Alzheimer’s disease diagnosis and mini-mental state examination score prediction separately and ignore the relation between these two tasks. To address this challenging problem, we propose a novel multi-task learning method, which uses feature interaction to explore the relationship between Alzheimer’s disease diagnosis and mini-mental state examination score prediction. In our proposed method, features from each task branch are firstly decoupled into candidate and non-candidate parts for interaction. Then, we propose feature sharing module to obtain shared features from candidate features and return shared features to task branches, which can promote the learning of each task. We validate the effectiveness of our proposed method on multiple datasets. In Alzheimer’s disease neuroimaging initiative 1 dataset, the accuracy in diagnosis task and the root mean squared error in prediction task of our proposed method is 87.86% and 2.5, respectively. Experimental results show that our proposed method outperforms most state-of-the-art methods. Our proposed method enables accurate Alzheimer’s disease diagnosis and mini-mental state examination score prediction. Therefore, it can be used as a reference for the clinical diagnosis of Alzheimer’s disease, and can also help doctors and patients track disease progression in a timely manner.