Trapping and manipulating micro-size particles using optical tweezers has contributed to many breakthroughs in biology, materials science, and colloidal physics. However, it remains challenging to extend this technique to a few nanometers particles owing to the diffraction limit and the considerable Brownian motion of trapped nanoparticles. In this work, a nanometric optical tweezer is proposed by using a plasmonic nanocavity composed of the closely spaced silver coated fiber tip and gold film. It is found that the radial vector mode can produce a nano-sized near field with the electric-field intensity enhancement factor over 103 through exciting the plasmon gap mode in the nanocavity. By employing the Maxwell stress tensor formalism, we theoretically demonstrate that this nano-sized near field results in a sharp quasi-harmonic potential well, capable of stably trapping 2 nm quantum dots beneath the tip apex with the laser power as low as 3.7 mW. Further analysis reveals that our nanotweezers can stably work in a wide range of particle-to-tip distances, gap sizes, and operation wavelengths. We envision that our proposed nanometric optical tweezers could be compatible with the tip-enhanced Raman spectroscopy to allow simultaneously manipulating and characterizing single nanoparticles as well as nanoparticle interactions with high sensitivity.