Recent advances in experiments have enabled the measurement of γ-decay from giant and pygmy resonances to low-lying states, establishing this technique as a unique probe for nuclear structure. However, a microscopic description of γ-decay to low-lying states in superfluid nuclei is still lacking. We develop the Skyrme quasiparticle vibration (QPVC) model to calculate γ-decay widths between vibrational states. This model treats initial and final states as quasiparticle random phase approximation (QRPA) phonons and includes all the second-order diagrams for the interaction between the quasiparticles and the phonons, while consistently accounting for the polarization processes. The same Skyrme functional is employed for the ground state and the interaction vertices. As a timely application, the γ-decay width from the giant dipole resonance to the 2^+_1 state in 140Ce is calculated, which has recently been measured at the high intensity γ-ray source (HIγS). For the 4 Skyrme functionals we used, the total width of the collective dipole states in GDR region is 200-420 eV and the corresponding branching ratio is 0.75-1.20%. The polarization effect, extracted microscopically, agrees in trend with the macroscopic Bohr-Mottelson formula.