Mild cognitive impairment (MCI) is difficult to diagnose due to its subtlety. Recent emergence of advanced network analysis techniques utilizing resting-state functional Magnetic Resonance Imaging (rs-fMRI) has made the understanding of neurological disorders more comprehensively at a whole-brain connectivity level. However, inferring effective brain connectivity from fMRI data is a challenging task, particularly when the ultimate goal is to obtain good control-patient classification performance. Incorporating sparsity into connectivity modeling can potentially produce results that are biologically more meaningful since most biologically networks are formed by a relatively few number of connections. However, this constraint, when applied at an individual level, will degrade classification performance due to inter-subject variability. To address this problem, we consider a constrained sparse linear regression model associated with the least absolute shrinkage and selection operator (LASSO). Specifically, we introduced sparsity into brain connectivity via l1-norm penalization, and ensured consistent non-zero connections across subjects via l2-norm penalization. Our results demonstrate that the constrained sparse network gives better classification performance than the conventional correlation-based network, indicating its greater sensitivity to early stage brain pathologies.