The Coulomb excitation of the soft-dipole mode (SDM) and its dynamical effect on the elastic scattering of halo nuclei, He-6 and Li-11 at E(lab)/A(P)=5 similar to 70 MeV, are investigated in the microscopic coupled-channel (CC) method. The Goldhaber-Teller (GT) model is employed to calculate the transition density for SDM. The proton and neutron density distributions as well as the dipole-transition strengths, which are the input to the GT model, are given by the coupled-rearrangement-channel variational method based on an a + n + n three-body model for He-6, and by a Li-9 + dineutron two-cluster-model calculation for Li-11. The results of the CC calculations show that the effect of the Coulomb excitation of SDM on the elastic scattering is suite significant, while the nuclear contribution is relatively small. We also investigate the characteristics of the Coulomb-dissociation cross sections, such as the energy dependence and the target dependence in the same model.