We numerically investigate the coupling efficiency of a single self-assembled quantum dot to a metallic slot waveguide in the presence of leaky plasmonic modes. Leaky plasmonic modes refer to radiation modes with plasmonic features, resulting from the inhomogeneity of the ielectric environment in which the metallic slot waveguide is embedded. Compared to the ideal case of a homogenous dielectric environment, the coupling efficiency of an emitter to a metallic slot waveguide is significantly reduced. We attribute the reduction to the coupling to leaky plasmonic modes. By increasing the refractive index of the coating layer to minimize the impacts from the leaky plasmonic modes, we find that the coupling efficiency of the quantum dot to the single mode supported by the metallic slot waveguide can be enhanced by more than a factor 2.