A 325-MHz superconducting half-wave resonator has been designed with β = 0.51. Three shapes of the inner conductors(race track, ring shape and elliptical shape) were optimized to decrease the peak electromagnetic fields and minimize the dissipated RF power on the cavity walls. In order to suppress the operation frequency shift caused by fluctuations of the helium pressure and maximize the tuning ranges, the frequency shifts and mechanical properties were studied on the electric and magnetic areas. The helium vessel was designed to keep the mechanical structure as robust as possible. A 325-MHz superconducting half-wave resonator has been designed with β = 0.51. Three shapes of the inner conductors (race track, ring shape and elliptical shape) were optimized to decrease the peak electromagnetic fields and minimize the dissipated RF power on the cavity In order to suppress the operation frequency shift caused by fluctuations of the helium pressure and maximize the tuning ranges, the frequency shifts and mechanical properties were studied on the electric and magnetic areas. The helium vessel was designed to keep the mechanical structure as robust as possible