Functional brain network (FBN) provides an effective biomarker for understanding brain activation patterns, which also improve the diagnostic criteria for neurodegenerative diseases or the information transmission of brain. Unfortunately, despite its efficiency, FBN still suffers several challenges for accurately estimate the biological meaningful or discriminative FBNs, under the poor quality of functional magnetic resonance imaging (fMRI) data as well as the limited understanding of human brain. Hence, there still a motivation to alleviate those issues above, it is currently still an open field to discover. In this paper, a novel FBN estimation model based on group similarity constraints is proposed. In particular, we extend the FBN estimation model to the tensor form and incorporate the trace-norm regularizer for formulating the group similarity constraint. In order to verify the proposed method, we conduct experiments on identifying Mild Cognitive Impairments (MCIs) from normal controls (NCs) based on the estimated FBNs. The experimental results illustrated that the proposed method can construct a more discriminative brain network.Consequently, we achieved an 91.97% classification accuracy which outperforms the baseline methods. The post hoc analysis further shown more biologically meaningful functional brain connections obtained by our proposed method.