Plasmonic nanostructures that support surface plasmon (SP) resonance potentially provide a route for the development of nanoengineered nonlinear optical media. In this work, a novel plasmonic particle-in-cavity nanoantenna (PIC-NA) is proposed. The second harmonic generation (SHG) of the PIC-NA under strong localized SP resonance is systematically analyzed by a self-consistent numerical solution based on boundary element method (BEM). The developed method solves the fundamental field and second harmonic (SH) field together iteratively to capture their mutual coupling. Strong enhancement of SHG from PIC-NA is achieved. The SHG enhancement factor is around four orders of magnitude, which is much higher than those achieved in literatures. Moreover, unidirectional SH radiation for the asymmetric PIC-NA is realized. Its emission direction can be controlled by the location of the nanosphere. The proposed novel plasmonic PIC-NA functions as the new synthetic second-order nonlinear optical material that has promising applications in the nonlinear sensing, spectroscopy and frequency generation.