Clues to a planet's geologic history are contained in its interior structure, particularly its core. We detected reflections of seismic waves from the core-mantle boundary of Mars using InSight seismic data and inverted these together with geodetic data to constrain the radius of the liquid metal core to 1830 +/- 40 kilometers. The large core implies a martian mantle mineralogically similar to the terrestrial upper mantle and transition zone but differing from Earth by not having a bridgmanite-dominated lower mantle. We inferred a mean core density of 5.7 to 6.3 grams per cubic centimeter, which requires a substantial complement of light elements dissolved in the iron-nickel core. The seismic core shadow as seen from InSight's location covers half the surface of Mars, including the majority of potentially active regions-e.g., Tharsis-possibly limiting the number of detectable marsquakes.