To investigate the differences in functional brain network structures between patients with a high level of generalized anxiety disorder (HGAD) and those with a low level of generalized anxiety disorder (LGAD), a resting-state electroencephalogram (EEG) was recorded in 30 LGAD patients and 21 HGAD patients. Functional connectivity between all pairs of brain regions was determined by the Phase Lag Index (PLI) to construct a functional brain network. Then, the characteristic path length, clustering coefficient, and small world were calculated to estimate functional brain network structures. The results showed that the PLI values of HGAD were significantly increased in alpha2, and significantly decreased in the theta and alpha1 rhythms, and the small-world attributes for both HGAD patients and LGAD patients were less than one for all the rhythms. Moreover, the small-world values of HGAD were significantly lower than those of LGAD in the theta and alpha2 rhythms, which indicated that the brain functional network structure would deteriorate with the increase in generalized anxiety disorder (GAD) severity. Our findings may play a role in the development and understanding of LGAD and HGAD to determine whether interventions that target these brain changes may be effective in treating GAD.