Alzheimer's disease (AD) is characterized by gradual neurodegeneration and loss of brain function, especially for memory during early stages. Regression analysis has been widely applied to AD research to relate clinical and biomarker data such as predicting cognitive outcomes from MRI measures. In particular, sparse models have been proposed to identify the optimal imaging markers with high prediction power. However, the complex relationship among imaging markers are often overlooked or simplified in the existing methods. To address this issue, we present a new sparse learning method by introducing a novel network term to more flexibly model the relationship among imaging markers. The proposed algorithm is applied to the ADNI study for predicting cognitive outcomes using MRI scans. The effectiveness of our method is demonstrated by its improved prediction performance over several state-of-the-art competing methods and accurate identification of cognition-relevant imaging markers that are biologically meaningful.