An asymmetric plasmonic slot waveguide (APSW) for efficient phase-matched third harmonic generation (THG) is proposed and demonstrated theoretically. Nonlinear organic material DDMEBT polymer is integrated into the bottom of the metallic slot, while silicon is used to fill the top of the slot. We introduce the rigorous coupled-mode equations of THG in the lossy APSW and apply them to optimize the waveguide geometry. Taking advantage of the surface plasmon polaritons (SPPs), the electric fields can be tightly confined in the metallic slot region and the nonlinear effect is greatly enhanced accordingly. Then, we investigate the relationships between THG efficiency and parameters such as slot width and height, phase matching condition (PMC), modal overlap related nonlinear parameter, figure-of-merit, pump power and detuning. With the proposed asymmetric waveguide, we demonstrate a high THG conversion efficiency of 4.88 × 10(-6) with a pump power of 1 W and a detuning constant of -36 m(-1) at a waveguide length of 10.65 ����m.