The creep behaviors of pure magnesium in different states at the temperatures 75~200℃ under stresses 15~40MPa were studied. The results indicates that the grain size has remarkable effect on the creep behavior. The as-cast magnesium has low creep rate with coarse column crystals. However, the creep rate increases significantly as the grains become fine equiaxed due to dynamic recrystallization after extrusion and deceases when the grains coarsen after anneale-treatments. The stress exponents lie in the range 4.3-4.9 under low stresses,which is consistent with the “Five-Power-Law” suggesting the creep is dislocation climb-controlled. However, the values of over 7 under high stresses indicate power-law breakdown. The apparent activation energies range from 76.0kJ/mol to 89.4kJ/mol. According to the stress exponents and the activation energies as well as the microstructure analysis during creep, the creep are affected by dislocation climb, grain boundary sliding and twinning, among which the former two play dominant role.