Magnesium has a hcp lattice structure, in which insufficient independent slip systems are available to accommodate applied plastic deformation at room temperature. The ductility of Mg is intimately related to the fundamental behaviors of pyramidal <c+a> dislocations, which are the major contributor to c-axis strain. In this study, the motion of <c+a> edge dislocation on the second-order pyramidal plane in Mg under external shear stress of different magnitudes and directions are simulated by molecular dynamics at 300 K, and the motion and structural evolution of dislocations are studied. The results show that the effective shear stress causing dislocation motion is lower than the external applied one and the dislocation velocity increases linearly with increasing applied shear stress. Under the same level of external shear stress, the dislocation velocity in shearing leading to c-axis tension deformation is higher than that for shearing leading to c-axis compression, and in both cases the corresponding viscous drag coefficients are significantly higher than those for basal and prismatic edge dislocations at the same temperature. The tension-compression asymmetry of dislocation motion is essentially related to the effect of applied shear stress on the extended dislocation width.