We used single-cell genomic approaches to map DNA copy number variation (CNV) in neurons obtained from human induced pluripotent stem cell (hiPSC) lines and postmortem human brains. We identified aneuploid neurons, as well as numerous subchromosomal CNVs in euploid neurons. Neurotypic hiPSC-derived neurons had larger CNVs than fibroblasts, and several large deletions were found in hiPSC-derived neurons but not in matched neural progenitor cells. Single-cell sequencing of endogenous human frontal cortex neurons revealed that 13 to 41% of neurons have at least one megabase-scale de novo CNV, that deletions are twice as common as duplications, and that a subset of neurons have highly aberrant genomes marked by multiple alterations. Our results show that mosaic CNV is abundant in human neurons.