The aim of this study was to predict the results of superplastic forming on magnesium alloy, by considering the grain growth using numerical simulations. Superplastic behavior of AZ31 alloy was investigated through a set of uniaxial tensile tests that cover the forming temperatures ranges from 375 to $450^{circ}C$. All the material parameters in the model, which consists of a constitutive equation and a grain growth equation, were determined. The model was used in the finite element analysis for uniaxial tensile tests and superplastic blow forming, through a user-subroutine available within ABAQUS. From this study, the effect of grain growth during forming was evaluated. The results show that it is essential to include the effect of grain growth in predicting the behavior during superplastic forming of this magnesium alloy.