Plasmonic nanocavities offer prospects for the amplification of inherently weak nonlinear responses at subwavelength scales. However, constructing these nanocavities with tunable modal volumes and reduced optical losses remains an open challenge in the development of nonlinear nanophotonics. Herein, we design and fabricate three-dimensional (3D) metal-dielectric-metal (MDM) plasmonic nanocavities that are capable of amplifying second-harmonic lights by up to three orders of magnitude with respect to dielectric-metal counterparts. In combination with experimental estimations of quantitative contributions of constituent parts in proposed 3D MDM designs, we further theoretically disclose the mechanism governing this signal amplification. We discover that this phenomenon can be attributed to the plasmon hybridization of both dipolar plasmon resonances and gap cavity resonances, such that an energy exchange channel can be attained and helps expand modal volumes while maintaining strong field localizations. Our results may advance the understanding of efficient nonlinear harmonic generations in 3D plasmonic nanostructures.