We report the tetrad phase vortex structure in the scattered surface plasmon polariton (SPP) field produced by a silver nano-ring-slit with linearly polarized illumination. In the experiment, Mach-Zehnder type interferometer is constructed in which a microscopic objective (MO) is used to collect and image the scattered SPP field, and the phase map is extracted by Fourier transform of the interference intensity. To explain the formation of the tetrad phase vortices in the central area of the ring, we propose an empirical model for the ring-slit-excited SPP source field by trial calculations with the Huygens-Fresnel principle for SPP propagations. It is shown that the azimuthal variation of the amplitude of the source SPP is roughly a half of a constant base, and the variation of the phase is a little greater than π/2. The intensity and the phase distributions of the SSP field calculated with the formulations of this model phenomenologically conform the experimental results.