Our brain is a complex network in which information is continuously processed and transported between spatially distributed but functionally linked regions. Recent studies have shown that the functional connections of the brain network are organized in a highly efficient small-world manner, indicating a high level of local neighborhood clustering, together with the existence of more long-distance connections that ensure a high level of global communication efficiency within the overall network. Such an efficient network architecture of our functional brain raises the question of a possible association between how efficiently the regions of our brain are functionally connected and our level of intelligence. Examining the overall organization of the brain network using graph analysis, we show a strong negative association between the normalized characteristic path length lambda of the resting-state brain network and intelligence quotient (IQ). This suggests that human intellectual performance is likely to be related to how efficiently our brain integrates information between multiple brain regions. Most pronounced effects between normalized path length and IQ were found in frontal and parietal regions. Our findings indicate a strong positive association between the global efficiency of functional brain networks and intellectual performance.