Functional brain network (FBN) provides an effective biomarker for understanding brain activation patterns and a diagnostic criterion for neurodegenerative diseases detections. Unfortunately, it remains challenges to estimate the biologically meaningful or discriminative FBNs accurately, because of the poor quality of functional magnetic resonance imaging data or our limited understanding of human brain. In this study, a novel FBN estimation model based on group similarity prior was proposed. In particular, we extended the FBN estimation model to tensor form and incorporated the tensor trace-norm regularizer to formulate the group similarity constraint. To verify the proposed method, we conducted experiments on identifying mild cognitive impairments (MCIs) from normal controls (NCs) based on the estimated FBNs. Experimental results illustrated that our method is effective in modeling FBNs. Consequently, we achieved 91.97% classification accuracy, outperforming the state-of-the-art methods. The post hoc analysis further demonstrated that more biologically meaningful functional brain connections were obtained using our proposed method.