Alzheimer's disease (AD) is a neurodegenerative disorder characterized by progressive impairment of memory and other cognitive functions. Regression analysis has been studied to relate neuroimagingmeasures to cognitive status. However, whether these measures have further predictive power to infer a trajectory of cognitive performance over time is still an under-explored but important topic in AD research. We propose a novel high-order multi-task learning model to address this issue. The proposed model explores the temporal correlations existing in imaging and cognitive data by structured sparsity-inducing norms. The sparsity of the model enables the selection of a small number of imaging measures while maintaining high prediction accuracy. The empirical studies, using the longitudinal imaging and cognitive data of the ADNI cohort, have yielded promising results.