Abstract Motivation Improvements in DNA sequencing technology and computational methods have led to a substantial increase in the creation of high-quality genome assemblies of many species. To understand the biology of these genomes, annotation of gene features and other functional elements is essential; however, for most species, only the reference genome is well-annotated. Results One strategy to annotate new or improved genome assemblies is to map or ‘lift over’ the genes from a previously annotated reference genome. Here, we describe Liftoff, a new genome annotation lift-over tool capable of mapping genes between two assemblies of the same or closely related species. Liftoff aligns genes from a reference genome to a target genome and finds the mapping that maximizes sequence identity while preserving the structure of each exon, transcript and gene. We show that Liftoff can accurately map 99.9% of genes between two versions of the human reference genome with an average sequence identity >99.9%. We also show that Liftoff can map genes across species by successfully lifting over 98.3% of human protein-coding genes to a chimpanzee genome assembly with 98.2% sequence identity. Availability and implementation Liftoff can be installed via bioconda and PyPI. In addition, the source code for Liftoff is available at https://github.com/agshumate/Liftoff. Supplementary information Supplementary data are available at Bioinformatics online.