Neuroimaging markers have been widely used to predict the cognitive functions relevant to the progression of Alzheimer's disease (AD). Most previous studies identify the imaging markers without considering the brain structural correlations between neuroimaging measures. However, many neuroimaging markers interrelate and work together to reveal the cognitive functions, such that these relevant markers should be selected together as the phenotypic markers. To solve this problem, in this paper, we propose a novel network constrained feature selection (NCFS) model to identify the neuroimaging markers guided by the structural brain network, which is constructed by the sparse representation method such that the interrelations between neuroimaging features are encoded into probabilities. Our new methods are evaluated by the MRI and AV45-PET data from ADNI-GO and ADNI-2 (Alzheimer's Disease Neuroimaging Initiative). In all cognitive function prediction tasks, our new NCFS method outperforms other state-of-the-art regression approaches. Meanwhile, we show that the new method can select the correlated imaging markers, which are ignored by the competing approaches.