Permanent magnet (PM) motors that employ rare-earth magnets containing dysprosium (Dy) are used in electric and hybrid electric vehicles. However, it is desirable to reduce the amount of Dy used since it is expensive. This study investigates the rotor structure of a PM synchronous motor with a Dy-free rare-earth magnet. Flux barrier shapes and PM thicknesses that enhance the irreversible demagnetization are investigated. In addition, a rotor structure that improves the irreversible demagnetization is proposed. We demonstrate that the proposed rotor structure without Dy improves the irreversible demagnetization.