The design of a vertical directional coupler between a three-dimensional plasmonic slot waveguide and a silicon waveguide is theoretically investigated in detail. It consists of two steps: the design of isolated plasmonic slot waveguide and silicon waveguide and the determination of the gap between the two waveguides and the length of a coupling region. The designed structure transfers 70.8% of the power carried by the silicon waveguide mode to the plasmonic slot waveguide mode when the gap is 150 nm and the coupling length is 2.14 μm. The wavelength dependence of our vertical directional coupler is also studied. The analysis shows that the amount of the transferred power changes slightly over a very wide wavelength range between 1.40 μm and 1.61 μm. Moreover, if we employ the fabrication technology for silicon photonics, it is quite tolerant to the variation of the length of its coupling section. Finally, the vertical directional coupler is considered for a polarizer.