How the human brain evolved has attracted tremendous interests for decades. Motivated by case studies of primate-specific genes implicated in brain function, we examined whether or not the young genes, those emerging genome-wide in the lineages specific to the primates or rodents, showed distinct spatial and temporal patterns of transcription compared to old genes, which had existed before primate and rodent split. We found consistent patterns across different sources of expression data: there is a significantly larger proportion of young genes expressed in the fetal or infant brain of humans than in mouse, and more young genes in humans have expression biased toward early developing brains than old genes. Most of these young genes are expressed in the evolutionarily newest part of human brain, the neocortex. Remarkably, we also identified a number of human-specific genes which are expressed in the prefrontal cortex, which is implicated in complex cognitive behaviors. The young genes upregulated in the early developing human brain play diverse functional roles, with a significant enrichment of transcription factors. Genes originating from different mechanisms show a similar expression bias in the developing brain. Moreover, we found that the young genes upregulated in early brain development showed rapid protein evolution compared to old genes also expressed in the fetal brain. Strikingly, genes expressed in the neocortex arose soon after its morphological origin. These four lines of evidence suggest that positive selection for brain function may have contributed to the origination of young genes expressed in the developing brain. These data demonstrate a striking recruitment of new genes into the early development of the human brain.