High-efficient, plasmon-enhanced nonlinear phenomena based on hybrid nanostructures, which combine nonlinear dielectrics with plasmonic metals, are of fundamental importance for various applications ranging from all-optical switching to imaging or bio-sensing. However, the high loss of the excitation energy in nanostructures and the poor spatial overlap between the plasmon enhancement and the bulk of nonlinear materials largely limit the operation of plasmon-enhanced nonlinear effects, resulting in low nonlinear conversion efficiency. Here, we design and fabricate a ZnO-covered, 2D silver-bowl array, which can serve as an efficient platform for plasmon-enhanced second-harmonic generation (PESHG). Validated by experiments and simulations, we demonstrate that the high spatial overlap between the near-field enhancement and the ZnO film plays the key role for this nanostructure-based PESHG process. The enhancement mainly originates from the fundamental wavelength-derived plasmon resonance, providing an enhancement factor of approximately 33 times. These results achieved pave the way for future applications, which require localized light sources at nanoscale.