Comparison of the Neanderthal genomes with those of modern humans has indicated that there has been substantial introgression of Neanderthal genomic sequences due to interbreeding, before Neanderthals were wiped out by modern humans who had migrated into Europe. Here we have analyzed human haplotype blocks associated with cognitive traits in genome-wide association studies (GWAS) and show that there has been significant depletion of Neanderthal alleles in these blocks, but not blocks associated with other GWAS traits. We also show that many of these haplotype blocks express lncRNAs that are expressed in the brain, especially in the cerebral cortex, and are developmentally regulated in humans. These lncRNAs likely emanate from enhancers and are prime mechanistic candidates for the cognitive advantages of modern humans that helped to outcompete Neanderthals and mixed ancestors lacking these advantages.