We theoretically investigate the quadratic nonlinear property of a silicon-organic hybrid plasmonic waveguide with a thin polymer layer deposited on top of a silicon slab and covered by a metal cap. Due to the hybridization property of the waveguide modes, efficient phase-matched second harmonic generation (SHG) from mid-infrared (IR) (~3.1 μm) to near-IR (~1.55 μm) wavelengths are achieved with a small fabrication-error sensitivity (225 nm ≤ tolerated waveguide width ≤ 378 nm) and a large bandwidth (Δλ=100 nm). The SHG yield is as large as 8.8% for a pumping power of 100 mW.