The present study was aimed to evaluate resting-state functional connectivity and topological properties of brain networks in narcolepsy patients compared with healthy controls. Resting-state fMRI was performed in 26 adult narcolepsy patients and 30 matched healthy controls. MRI data were first analyzed by group independent component analysis, then a graph theoretical method was applied to evaluate the topological properties in the whole brain. Small-world network parameters and nodal topological properties were measured. Altered topological properties in brain areas between groups were selected as region-of-interest seeds, then the functional connectivity among these seeds was compared between groups. Partial correlation analysis was performed to evaluate the relationship between the severity of sleepiness and functional connectivity or topological properties in the narcolepsy patients. Twenty-one independent components out of 48 were obtained. Compared with healthy controls, the narcolepsy patients exhibited significantly decreased functional connectivity within the executive and salience networks, along with increased functional connectivity in the bilateral frontal lobes within the executive network. There were no differences in small-world network properties between patients and controls. The altered brain areas in nodal topological properties between groups were mainly in the inferior frontal cortex, basal ganglia, anterior cingulate, sensory cortex, supplementary motor cortex, and visual cortex. In the partial correlation analysis, nodal topological properties in the putamen, anterior cingulate, and sensory cortex as well as functional connectivity between these regions were correlated with the severity of sleepiness (sleep latency, REM sleep latency, and Epworth sleepiness score) among narcolepsy patients. Altered connectivity within the executive and salience networks was found in narcolepsy patients. Functional connection changes between the left frontal cortex and left caudate nucleus may be one of the parameters describing the severity of narcolepsy. Changes in the nodal topological properties in the left putamen and left posterior cingulate, changes in functional connectivity between the left supplementary motor area and right occipital as well as in functional connectivity between the left anterior cingulate gyrus and bilateral postcentral gyrus can be considered as a specific indicator for evaluating the severity of narcolepsy.