The strong coupling between single quantum emitters and resonant optical micro/nanocavities is beneficial for understanding light and matter interactions. Here, we propose a plasmonic nanoantenna placed on a metal film to achieve an ultra-high electric field enhancement in the nanogap and an ultra-small optical mode volume. The strong coupling between a single quantum dot (QD) and the designed structure is investigated in detail by both numerical simulations and theoretical calculations. When a single QD is inserted into the nanogap of the silver nanoantenna, the scattering spectra show a remarkably large splitting and anticrossing behavior of the vacuum Rabi splitting, which can be achieved in the scattering spectra by optimizing the nanoantenna thickness. Our work shows another way to enhance the light/matter interaction at a single quantum emitter limit, which can be useful for many nanophotonic and quantum applications.