Conventional HEV motors use neodymium magnets with added heavy rare earths, to realize high output and size reduction. However, deposits of heavy rare earths such as Dysprosium (Dy) and Terbium (Tb) are unevenly distributed, so it is important to reduce the amount used, because of supply issue and material cost. In this paper, the application of a heavy rare earth-free magnet is considered on the new motor for a two-motor hybrid system. Compared to conventional neodymium magnets, heavy rare earth free magnets tend to have low coercivity. Also, heavy rare earth-free magnet have low thermal durability, so it is not easy to apply them to motors for a two-motor hybrid system, which requires high output and small size. The motor requires twice as much torque and six times output than one-motor hybrid system. Increase demagnetization resistance and magnet cooling performance is studied by development of the new motor. With the new rotor structure, a magnetic circuit suitable for the magnetic property of heavy rare earth-free magnet was designed, and demagnetization resistance property is raised 24%. Also, the new motor cooling system is a shaft cooling structure, which uses centrifugal force to supply refrigerant to the interior of the rotor yoke, achieving a 23% increase in magnet cooling performance. This technology succeeded in applying heavy rare earth-free magnet to the motor for a two-motor hybrid system, while maintaining high power density.