(MgO)12 in a tube structure is one of the magic number clusters of (MgO)n and exhibits particular stability. To study the electric field effect on the hydrogen storage properties of (MgO)12, the H2 adsorption behavior on the surface of the tube (MgO)12 in an external electric field is explored at the level of B3LY/6-31G**. In the external electric field, the (MgO)12 keeps the frame of tube structure but with little distortion, implying that the (MgO)12 cluster can sustain the strong electric field for hydrogen storage. The NBO analysis also indicates that (MgO)12 is polarized by the external electric field; and its dipole momenta increase to 9.21 and 19.39 Debye at the field intensities of 0.01 and 0.02 a.u., respectively. Without the external electric field, H2 can be adsorbed on Mg atoms in the end on modes, while on O atoms in the top on modes. When the external electric field is applied, whether H2 is adsorbed on Mg or O atoms, the stable adsorption structures are all top on modes and the molecular orientation of H2 is turned to the direction of the external electric field. Because (MgO)12 and H2 are effectively polarized by the external electric field, the adsorption strength of H2 on some adsorption sites are enhanced remarkably. The adsorption energies of H2 on the three-coordinated Mg/O are promoted from 0.08/0.06 eV in free field to 0.12/0.11 eV and 0.20/0.26 eV at field intensities of 0.01 a.u. and 0.02 a.u., respectively. Electronic structure analysis reveals that when H2 is adsorbed on Mg atoms, this process denotes charges moving to the cluster, and the improvement of adsorption interaction of H2 on Mg atoms is mainly due to the polarization effect. While the adsorption on O atoms, on the one hand implies the polarization effect of O anion is stronger than that of Mg cation, on the other hand, H2 receives charges from (MgO)12 and its valence orbitals also take part in the bonding with the valence orbitals of the cluster. Thus the structures of H2 adsorbed on O atoms are more stable. In an external electric field, (MgO)12 can adsorb sixteen H2 molecules at most, and the corresponding mass density of hydrogen storage reaches 6.25wt%.