The properties of guided plasmon polaritons supported by a triangular metallic waveguide are presented. The waveguide examined is a metal core with equilateral triangular cross section embedded in an infinite lossless dielectric media. Based on the rotation symmetry of the waveguide, the sketch of the supported fundament modes is given. The fundamental modes can be constructed by a proper combination of the corner modes and surface modes, which can be supported by isolated metal corners and metallic-dielectric interface respectively. The mode properties of the metallic waveguide, e.g., the dispersion and propagation length with the size of the metal core, mode field orientation and field distribution profiles are addressed by using a finite element method. The numerical singularities of the optical field are removed by smoothing the corners with an appropriate arc at the nano meter scale. The guided modes supported by the structure are determined and characterized for both subwavelength and suprawavelength. We find that the corner modes exist in both regimes, while the surface modes only appear in the suprawavelenth. Our results also show that the mode properties preserve a certain kind of symmetry of the waveguides. The degenerate modes exist both for the corner guided modes and for surface guided modes. The first fundamental corner modes is a polarization-independent mode without the cut-off size of the waveguides. Calculations also show how sensitively the mode changes with the corner sharpness. The propagation constant of the corner modes is sensitive to the corner sharpness, while the side modes are unaffected.