We conducted a feasibility study for producing a high-purity medical radioisotope Cu-64 from natural zinc with accelerator-based neutrons. Cu-64 isotopes were produced via the Zn-64(n,p) reaction. The accelerator-based neutrons were generated via the C(d,n) reaction using low-energy deuterons of 9 and 12 MeV on a 1-mm-thick carbon target. First, the production purity was estimated using the evaluated nuclear data library JENDL-4.0 and our previously measured thick target neutron yield. We found that even when natural zinc was used as the starting material, significantly high-purity Cu-64 could be obtained. Next, irradiation experiments for producing Cu-64 using natural zinc were conducted at Kyushu University Tandem Laboratory, with the amounts of Cu-64 isotopes and other gamma-emission nuclides measured by a high-purity germanium detector. As a result, high-purity Cu-64 isotopes of 1.11(49)x 10(0) and 3.70 (17) x 10(0) Bq/g/C were produced with incident deuteron energies of 9 and 12 MeV, respectively.