Cognitive functional networks such as the default-mode network (DMN), frontal-parietal network (FPN), and salience network (SN), are key networks of the human brain. Here, we show that the distinct rapid evolutionary cortical expansion of cognitive networks in the human brain, and most pronounced the DMN, runs parallel with high expression of genes important for human evolution (so-called HAR genes). Comparative gene expression examination then shows that HAR genes are more differentially expressed in cognitive networks in humans compared to the chimpanzee and macaque. Genes with distinct high expression in the DMN display broad involvement in the formation of synapses and dendrites. Next, we performed a genome-wide association analysis on functional MRI data, and show that HAR genes are associated with individual variations in DMN functional connectivity in today's human population. Finally, gene-set analysis suggests associations of HAR genes with intelligence, social cognition, and mental conditions such as schizophrenia and autism. Taken together, our results indicate that the expansion of higher-order functional networks and their cognitive properties have been an important locus of change in recent human brain evolution.