The structure-function coupling in brain networks has emerged as an important research topic in modern neuroscience. The structural network could provide the backbone of the functional network. The integration of the functional network with structural information can help us better understand functional communication in the brain. This paper proposed a method to accurately estimate the brain functional network enriched by the structural network from diffusion magnetic resonance imaging. First, we adopted a simplex regression model with graph-constrained Elastic Net to construct the functional networks enriched by the structural network. Then, we compared the constructed network characteristics of this approach with several state-of-the-art competing functional network models. Furthermore, we evaluated whether the structural enriched functional network model improves the performance for predicting the cognitive-behavioral outcomes. The experiments have been performed on 218 participants from the Human Connectome Project database. The results demonstrated that our network model improves network consistency and its predictive performance compared with several state-of-the-art competing functional network models.