Imaging genetics studies with large samples have identified many genes associated with brain functions and structures, but little is known about genes associated with brain functional and structural network properties. The current genome-wide association study (GWAS) examined graph theory measures of brain structural and functional networks with 497 healthy Chinese participants (17-28 years). Four genes (TGFB3, LGI1, TSPAN18 and FAM155A) were identified significantly associated with functional network global efficiency, two (NLRP6 and ICE2) with structural network global efficiency. Meta-analysis of structural and functional brain network property confirmed the 4 functional related genes and revealed two more (RBFOX1 and WWOX). These genes did not significantly associate with any single structural or functional connectivity. They were reported significantly associated with regional brain structural or functional measurements in the UK Biobank project; and showed differential gene expression level between low and high structure-function coupling regions according to Allen Human Brain Atlas gene expression data. Taken together, our results suggest that brain structural and functional networks had shared and unique genetic bases, consistent with the notion of many-to-many structure-function coupling of the brain.