We investigate the change of the neutron-skin thickness from parent to daughter nuclei involved in the cluster decay process. The neutron-skin thickness is obtained using self-consistent Hartree–Fock–Bogolyubov calculations based on Skyrme-SLy4 effective nucleon–nucleon interaction. The experimental data of the cluster decay modes observed to date indicate that the shell effect then the released energy play the predominate role of determining the spontaneous cluster decay modes. The effect of the change in the neutron-skin thickness from parent to daughter nuclei comes next to them. The cluster decay preferably proceeds to yield the least possible increase in the neutron-skin thickness of the daughter nucleus (δ n). δ n decreases when the isospin-asymmetry of the emitted cluster increases. The relative stability of the radioactive nucleus and its corresponding partial half-life increase for the cluster decays leading to a significant increase in the neutron-skin thickness.