Structural genomic variations represent a major driving force of evolution, and a burst of large segmental gene duplications occurred in the human lineage during its separation from nonhuman primates. SRGAP2, a gene recently implicated in neocortical development, has undergone two human-specific duplications. Here, we find that both duplications (SRGAP2B and SRGAP2C) are partial and encode a truncated F-BAR domain. SRGAP2C is expressed in the developing and adult human brain and dimerizes with ancestral SRGAP2 to inhibit its function. In the mouse neocortex, SRGAP2 promotes spine maturation and limits spine density. Expression of SRGAP2C phenocopies SRGAP2 deficiency. It underlies sustained radial migration and leads to the emergence of human-specific features, including neoteny during spine maturation and increased density of longer spines. These results suggest that inhibition of SRGAP2 function by its human-specific paralogs has contributed to the evolution of the human neocortex and plays an important role during human brain development.