In this paper, we propose a multi-task learning approach for predicting the progression of Alzheimer's disease (AD), known as the most common form of dementia. The vital challenge is to identify how the tasks are related and build learning models to capture such task relatedness. Unlike previous methods that assume low-rank structure, chase the predefined local temporal relatedness or utilize local approximation, we propose a novel penalty termed L ongitudinal S tability A djustment (LSA) to adaptively capture the intrinsic global temporal correlation among multiple time points and thus utilize the accumulated disease progression information. We combine LSA with sparse group Lasso to present a novel multi-task learning formulation to identify biomarkers closely related to cognitive measurement and predict AD progression. Two efficient algorithms are designed for large-scale dataset. Experimental results conducted on two AD data sets demonstrate our framework outperforms competing methods in terms of overall and each task performances. We also perform stability selection to identify stable biomarkers from the MRI feature set and analyze their temporal patterns in disease progression.