Visual cortical stroke patients may have hemianopia symptom, which affects a number of visual functions. Most studies on hemianopia stroke have mainly focused on cortical activation during visual stimulation, leaving the pattern of functional connectivity between different brain regions uncovered yet. In the present study, we investigate the resting neural networks of hemianopia stroke patients by graph theoretical analysis of functional brain networks constructed with phase synchronization indexes of multichannel electroencephalography (EEG) signals. Our results showed that although the global network topological metrics, i.e., weighted clustering coefficient and characteristic path length of patients and healthy controls are comparable, the left primary visual cortex of patients tend to be less active than that of age-matched healthy subjects. However, hemianopia patients showed greater activation in the ipsilesional (left) temporopolar and orbit frontal areas and the contralesional (right) associative visual cortex. These results may offer new insight into neural substrates of the hemianopia stroke, and the further study of neural plasticity and brain reorganization after hemianopia.