Strain rate dependence of a low-cycle fatigue property of AZ31 magnesium alloy is investigated. Low cycle fatigue tests under low strain rate at 6.2×10^-5s^-1 and 6.2×10^-4s^-1 are performed. The stress ratio and the maximum stress are set to -1/2 and 240MPa respectively. Fatigue life, plastic strain amplitude, inelastic strain energy density per cycle and strain rate dependence are investigated. As a result, the number of cycle to fracture decrease with decreasing the strain rate. The inelastic strain energy density per cycle increase with decreasing the strain rate. The relationship between the inelastic strain energy density per cycle and the number of cycle to fracture agree with energy based model.