Olfactory dysfunction (OD) is a common symptom in coronavirus disease 2019 (COVID-19) patients. Moreover, many neurological manifestations have been reported in these patients, suggesting central nervous system involvement. The default mode network (DMN) is closely associated with olfactory processing. In this study, we investigated the internetwork and intranetwork connectivity of the DMN and the olfactory network (ON) in 13 healthy controls and 22 patients presenting with COVID-19-related OD using independent component analysis and region of interest functional magnetic resonance imaging (fMRI) analysis. There was a significant correlation between the butanol threshold test (BTT) and the intranetwork connectivity in ON. Meanwhile, the COVID-19 patients with OD showed significantly higher intranetwork connectivity in the DMN, as well as higher internetwork connectivity between ON and DMN. However, no significant difference was found between groups in the intranetwork connectivity within ON. We postulate that higher intranetwork functional connectivities compensate for the deficits in olfactory processing and general well-being in COVID-19 patients. Nevertheless, the compensation process in the ON may not be obvious at this stage. Our results suggest that resting-state fMRI is a potentially valuable tool to evaluate neurosensory dysfunction in COVID-19 patients.