The researches of third harmonic generation (THG) and third-order parametric down-conversion (TPDC) always encounter the problem of phase mismatching with such a large frequency span. Waveguides modal dispersion is an effective tool to compensate the material dispersion. However, the nonlinear polarization form of THG or TPDC is an odd function that will be almost zero if the mode field distribution contains opposite sign components. Several asymmetric plasmonic slot waveguides infiltrated in nonlinear organic material (2-\[4(dimethylamino)phenyl\]-3-f\[4-(dimethylamino)phenyl\]ethynylgbuta-1,3-diene-1,1,4-tetracarbonitrile) (DDMEBT) with high third-order susceptibility are proposed. Silicon (Si) is used to fill the bottom metallic slot region to break the symmetry of the waveguide. Silver (Ag) is considered to be the metal medium due to its low loss. The needed phase-matching condition (PMC) is satisfied between the zeroth mode at fundamental frequency (FF) and the first mode at third harmonic (TH) by appropriate designing the waveguide geometrical parameters. The corresponding overlap factor for THG or TPDC is much larger than the symmetric distribution.