To explore the alterations of functional connectivity (FC) and connections within and between the subnetworks of the visual network and the default mode network in glaucoma. We applied the independent component analysis to obtain two resting-state networks (RSNs), which were the visual network and the default mode network (DMN), from the resting-state fMRI data of 25 primary open-angle glaucoma (POAG) patients and 25 well-matched normal controls. Then FC analysis was performed to obtain the altered FC within the RSNs, whereas the functional network connectivity (FNC) analysis was performed within and between these two RSNs. The abnormalities were correlated with clinical measures in glaucoma to investigate the abnormality-clinical relationship. FC analysis showed that the FC in the occipital pole of the visual network was decreased in POAG patients while no alterations were found in the FC of the DMN in patients. FNC analysis of connections within the RSNs found that two of the three connections within the visual network were decreased while no connection alterations were found within the DMN. FNC analysis of connections between these two RSNs found two increased connections and one decreased connection. The decreased connection between these two RSNs was positively correlated with the visual field mean deviation. These findings shed light on the importance of the reorganization of resting state networks in glaucoma mechanism, which may facilitate the understanding of glaucoma.