The generalized stacking fault (GSF) energies have been calculated for basal plane and prismatic plane in magnesium from first-principles. The calculation of the GSF energy is performed paying particular attention to the effects of the relaxation scheme of atomic configurations. It is investigated the stable stacking fault, that is not so clear on prismatic plane, from the GSF energy. Then the Peierls stress of a partial dislocation on basal plane, and of an edge dislocation on prismatic plane is obtained by recent analytical solution and calculated GSF energies. The magnitude of the Peierls stress is in good agreement with experimental measurement.