Emergence of advanced network analysis techniques utilizing resting-state functional magnetic resonance imaging (R-fMRI) has enabled a more comprehensive understanding of neurological disorders at a whole-brain level. However, inferring brain connectivity from R-fMRI is a challenging task, particularly when the ultimate goal is to achieve good control–patient classification performance, owing to perplexing noise effects, curse of dimensionality, and inter-subject variability. Incorporating sparsity into connectivity modeling may be a possible solution to partially remedy this problem since most biological networks are intrinsically sparse. Nevertheless, sparsity constraint, when applied at an individual level, will inevitably cause inter-subject variability and hence degrade classification performance. To this end, we formulate the R-fMRI time series of each region of interest (ROI) as a linear representation of time series of other ROIs to infer sparse connectivity networks that are topologically identical across individuals. This formulation allows simultaneous selection of a common set of ROIs across subjects so that their linear combination is best in estimating the time series of the considered ROI. Specifically, l1-norm is imposed on each subject to filter out spurious or insignificant connections to produce sparse networks. A group-constraint is hence imposed via multi-task learning using a l2-norm to encourage consistent non-zero connections across subjects. This group-constraint is crucial since the network topology is identical for all subjects while still preserving individual information via different connectivity values. We validated the proposed modeling in mild cognitive impairment identification and promising results achieved demonstrate its superiority in disease characterization, particularly greater sensitivity to early stage brain pathologies. The inferred group-constrained sparse network is found to be biologically plausible and is highly associated with the disease-associated anatomical anomalies. Furthermore, our proposed approach achieved similar classification performance when finer atlas was used to parcellate the brain space.