A nonlinear hybrid plasmonic slot waveguide composed of periodically poled lithium niobate (PPLN) and two separated silver films is investigated. The effective refractive index, propagation length, and energy confinement of the hybrid anti-symmetric mode in this waveguide are calculated using the structure parameters at the fundamental wavelength of \lambda=1550 nm and its second harmonic (SH) \lambda= 775 nm. Through the above indices, coupling efficiency (maximum SH conversion efficiency during propagation) and peak position (propagation location of the conversion efficiency) of SH generation are analyzed. Finally, higher conversion efficiency can be achieved at a shorter propagation distance by changing the waveguide into a tapered structure.