Discrete geometric method (DGM) is implemented for solving Maxwell's equations on plasmonic structures. Surface plasmons introduce non-derivable field components at the metallic/dielectric interface that can influence the accuracy of DGM. An analysis shows that the proper setting of material parameters at the interface can increase the accuracy of numerical solutions. Numerical examples with a structured mesh and an unstructured mesh provide further evidence for the fact that a proper interface treatment is important to obtain accurate results with relatively less degrees of freedom for the simulation of plasmonic effects with DGM. Coupling with its flexibility and explicit formulation, DGM can be used as an accurate and fast solver for problems involving complex plasmonic structures.