Background White matter hyperintensity (WMH) is one of the typical neuroimaging manifestations of cerebral small vessel disease (CSVD), and the WMH correlates closely to cognitive impairment (CI). CSVD patients with WMH own altered topological properties of brain functional network, which is a possible mechanism that leads to CI. This study aims to identify differences in the characteristics of some brain functional network among patients with different grades of WMH and estimates the correlations between these different brain functional network characteristics and cognitive assessment scores. Methods 110 CSVD patients underwent 3.0 T Magnetic resonance imaging scans and neuropsychological cognitive assessments. WMH of each participant was graded on the basis of Fazekas grade scale and was divided into two groups: (A) WMH score of 1-2 points (n = 64), (B) WMH score of 3-6 points (n = 46). Topological indexes of brain functional network were analyzed using graph-theoretical method. T-test and Mann-Whitney U test was used to compare the differences in topological properties of brain functional network between groups. Partial correlation analysis was applied to explore the relationship between different topological properties of brain functional networks and overall cognitive function. Results Patients with high WMH scores exhibited decreased clustering coefficient values, global and local network efficiency along with increased shortest path length on whole brain level as well as decreased nodal efficiency in some brain regions on nodal level (p < 0.05). Nodal efficiency in the left lingual gyrus was significantly positively correlated with patients' total Montreal Cognitive Assessment (MoCA) scores (p < 0.05). No significant difference was found between two groups on the aspect of total MoCA and Mini-mental State Examination (MMSE) scores (p > 0.05). Conclusion Therefore, we come to conclusions that patients with high WMH scores showed less optimized small-world networks compared to patients with low WMH scores. Global and local network efficiency on the whole-brain level, as well as nodal efficiency in certain brain regions on the nodal level, can be viewed as markers to reflect the course of WMH.