Hot compression tests on AZ40 magnesium alloy were conducted on a Gleeble 1500d hot simulation testing machine in a deformation temperature range of 330 ℃-420 ℃ and a strain rate range of 0.002-2 s-1. Hot deformation behaviors were investigated on the basis of the analysis of the flow stress-strain curves, constitutive equation, and processing map. The stress exponent and apparent activation energy were calculated to be 5.821 and 173.96 kJ/mol, respectively. Deformation twins and cracks located in grain boundaries were generated at 330 ℃ and 0.02 s-1, which are associated with a high strain rate and a limited number of available slip systems. With increasing temperature and decreasing strain rate, the twins disappeared and the degree of dynamic recrystallization increased. The alloy was completely dynamically recrystallized at 420 ℃ and 0.002 s-1, with a homogenous grain size of approximately 13.7 μm. The instability domains of the deformation behavior can be recognized by processing maps. By considering the processing maps and characterizing the microstructure, the optimum hot deformation parameters in this experiment were determined to be 420 ℃ and 0.002 s-1.