Brain network discovery has attracted much attention in recent years, which aims at inferring a set of cohesive regions (i.e., the network nodes) and the connectivity between these regions (i.e., the network edges) in brain from neuroimaging data (e.g., fMRI, PET scans). Previous methods on brain network discovery mainly focus on either estimating the connectivity based on predefined brain regions, or inferring the brain regions and connectivity independently. However, the tasks of discovering brain regions and their connectivity are highly related to each other and should be discovered collectively, instead of independently. In this work, we propose a coherent data-driven method called SGGL (Spectral Group Graphical Lasso) to derive the nodes and edges of a brain network simultaneously. We propose a screening strategy to reduce the time cost of solving the corresponding optimization problem. Extensive experiments are performed on both synthetic data and real data from ADHD-200 project. The results demonstrate the effectiveness of the proposed method.