Mild cognitive impairment (MCI) is an intermediate stage of brain cognitive decline, associated with increasing risk of developing Alzheimer's disease (AD). It is believed that early treatment of MCI could slow down the progression of AD, and functional brain network (FBN) could provide potential imaging biomarkers for MCI diagnosis and response to treatment. However, there are still some challenges to estimate a "good" FBN, particularly due to the poor quality and limited quantity of functional magnetic resonance imaging (fMRI) data from the target domain (i.e., MCI study). Inspired by the idea of transfer learning, we attempt to transfer information in high-quality data from source domain (e.g., human connectome project in this paper) into the target domain towards a better FBN estimation, and propose a novel method, namely NERTL (Network Estimation via Regularized Transfer Learning). Specifically, we first construct a high-quality network "template" based on the source data, and then use the template to guide or constrain the target of FBN estimation by a weighted l1-norm regularizer. Finally, we conduct experiments to identify subjects with MCI from normal controls (NCs) based on the estimated FBNs. Despite its simplicity, our proposed method is more effective than the baseline methods in modeling discriminative FBNs, as demonstrated by the superior MCI classification accuracy of 82.4% and the area under curve (AUC) of 0.910.