Laser-driven gamma-ray source potentially offers a compact, cost-effective, ultra-short, and ultra-bright alternative to conventional gamma-ray sources based on large-scale particle accelerators. Based on the laser-driven approach, we use multidimensional particle-in-cell simulations to demonstrate that a nanostructured double-layer target, which consists of a nanostructured foam coated on top of a metal substrate, can absorb laser energy into high-energy electrons in the nanostructured foam, and then efficiently convert it into copious gamma photons via the nonlinear Compton scattering process enabled by the solid-density substrate, which acts as a plasma mirror to reflect the laser pulse. The effects of different nanostructures in the foam target and the oblique laser incidence are presented. It is shown that the conversion efficiency of gamma photons increases when the size of nanoparticles decreases or the filling factor of nanoparticles increases in nanostructured foam target, but decreases when the laser incidence angle increases. At realistic conditions with nanostructured foam and non-normal incidence, the double-layer target still exhibits an unprecedentedly high conversion efficiency in high-energy gamma-ray production due to the laser reflection by the plasma mirror, which can be two and even three orders of magnitude higher than that of the single-layer target without the substrate using currently available lasers with intensity of 1021.