Enhancements up to four orders of magnitude for electric intensity and three orders of magnitude for magnetic intensity are realized in a novel 2D L-shaped nanocavity. This structure makes full use of the dimension confinement, cavity resonance and tip enhancement to increase the electromagnetic intensity. An impedance matching model is developed to design this cavity by regarding the cavity as a load impedance where electromagnetic fields are maximally enhanced when maximum electromagnetic energy is delivered to the load impedance. Our L-shaped nanocavity promises a variety of useful functionalities in sensing, nonlinear spectroscopy and signal processing.