The pursuit of a systematic frequency uncertainty beyond 10-18 clock has triggered a multitude of investigations on the multipolar and higher-order lattice light shifts.The Cd atom has been proposed as a new candidate for the development of a lattice clock because of its smaller blackbody radiation shift at room temperature.Here,we apply an improved combined method of the Dirac-Fock plus core polarization and relativistic configuration interaction methods to calculate the dynamic multipolar polarizabilities of the Cd clock states.The effects of the high-order core-polarization potentials on the energies,reduced matrix elements,and multipolar polarizabilities have been evaluated systematically.The detailed comparison with available literature demonstrates that taking into account of the high-order core-polarization potentials is a simple and effective approach to improve the results of atomic properties for heavy atoms.