The human forebrain has expanded in size and complexity compared to chimpanzees despite limited changes in protein-coding genes, suggesting that gene expression regulation is an important driver of brain evolution. Here, we identify a KRAB-ZFP transcription factor, ZNF558, that is expressed in human but not chimpanzee forebrain neural progenitor cells. ZNF558 evolved as a suppressor of LINE-1 transposons but has been co-opted to regulate a single target, the mitophagy gene SPATA18. ZNF558 plays a role in mitochondrial homeostasis, and loss-of-function experiments in cerebral organoids suggests that ZNF558 influences developmental timing during early human brain development. Expression of ZNF558 is controlled by the size of a variable number tandem repeat that is longer in chimpanzees compared to humans, and variable in the human population. Thus, this work provides mechanistic insight into how a cis-acting structural variation establishes a regulatory network that affects human brain evolution.