Carbon ions and protons from a double-layer target, a copper foil coated with a polymer exhibit non-Maxwellian spectral shapes, when an ultra-intense laser pulse with a high temporal contrast ratio was focused on the metal side of the target. The spectral shapes, showing strong reduction of low-energy ions, a high-energy island, and a modulated structure, are different from a typical thermal distribution usually obtained from a pure metal target in the laser acceleration of ions. In the case of C 6 + ion, a high-energy island with an energy spread of 0.5 MeV/u was observed, which is separated from the low-energy spectrum by 0.2 MeV/u. A modulation in the proton energy spectrum was observed, which leads to a secondary peak at 2.2 MeV/u in addition to a peak at a low energy of 1.5 MeV/u. The maximum energy obtained from the double-layer target at a laser intensity of 3 × 10 20 W/cm 2 is 3.4 MeV/u for C 6 + ions and 10 MeV/u for protons, which are higher than those obtained from a single metal foil by factors of 1.7 and 1.3, respectively. Such a spectral shape and energy enhancement could be accounted for by a bulk electrostatic field formed at the metal-polymer interface and multi-species interactions. These results show that the spectral shape of the ion beam can be tailored with an adequate structure of micrometer-thick target.