Adolescence represents an important period during which considerable changes in the brain take place, including increases in integrity of white matter bundles, and increasing efficiency of the structural brain network. A more efficient structural brain network has been associated with higher intelligence. Whether development of structural network efficiency is related to intelligence, and if so to which extent genetic and environmental influences are implicated in their association, is not known. In a longitudinal study, we mapped FA-weighted efficiency of the structural brain network in 310 twins and their older siblings at an average age of 10, 13, and 18 years. Age-trajectories of global and local FA-weighted efficiency were related to intelligence. Contributions of genes and environment were estimated using structural equation modeling. Efficiency of brain networks changed in a non-linear fashion from childhood to early adulthood, increasing between 10 and 13 years, and leveling off between 13 and 18 years. Adolescents with higher intelligence had higher global and local network efficiency. The dependency of FA-weighted global efficiency on IQ increased during adolescence (rph =0.007 at age 10; 0.23 at age 18). Global efficiency was significantly heritable during adolescence (47% at age 18). The genetic correlation between intelligence and global and local efficiency increased with age; genes explained up to 87% of the observed correlation at age 18. In conclusion, the brain's structural network differentiates depending on IQ during adolescence, and is under increasing influence of genes that are also associated with intelligence as it develops from late childhood to adulthood.