We show enhanced second-harmonic generation (SHG) from a hybrid metal-dielectric nanodimer consisting of an inorganic perovskite nanoparticle of barium titanate (BaTiO3) coupled to a metallic gold (Au) nanoparticle. BaTiO3-Au nanodimers of 100 nm/80 nm sizes are fabricated by sequential capillarity-assisted particle assembly. The BaTiO3 nanoparticle has a noncentrosymmetric crystalline structure and generates bulk SHG. We use the localized surface plasmon resonance of the gold nanoparticle to enhance the SHG from the BaTiO3 nanoparticle. We experimentally measure the nonlinear signal from assembled nanodimers and demonstrate an up to 15-fold enhancement compared to a single BaTiO3 nanoparticle. We further perform numerical simulations of the linear and SHG spectra of the BaTiO3-Au nanodimer and show that the gold nanoparticle acts as a nanoantenna at the SHG wavelength.