Subcortical regions can be functionally organized into connectivity networks and are extensively communicated with the cortex via reciprocal connections. However, most current research on subcortical networks ignores these interconnections, and networks of the whole brain are of high dimensionality and computational complexity. In this article, we propose a novel cofluctuation-guided subcortical connectivity network construction model based on edge-centric functional connectivity (FC). It is capable of extracting the cofluctuations between the cortex and subcortex and constructing dynamic subcortical networks based on these interconnections. Blind source separation approaches with domain knowledge are designed for dimensionality reduction and feature extraction. Great reproducibility and reliability were achieved when applying our model to two sessions of functional magnetic resonance imaging (fMRI) data. Cortical areas having synchronous communications with the cortex were detected, which was unable to be revealed by traditional node-centric FC. Significant alterations in connectivity patterns were observed when dealing with fMRI of subjects with and without Parkinson's disease, which were further correlated to clinical scores. These validations demonstrated that our model provided a promising strategy for brain network construction, exhibiting great potential in clinical practice.