The contribution due to the Debye screening to the dissolution of heavy-quark resonances is studied by using the two different binding potentials at finite temperature in a nonrelativistic approximation. The critical values of the Debye screening length are calculated. Our calculations show that the critical values of the Debye screening length depend on the forms of the quark binding potential at finite temperature. We also estimate the critical temperature for deconfinement of heavy-quark resonances. The effects of different quark binding potentials on the dissolution for heavy-quark resonances are discussed and compared to the previous results.