We describe a surface structure that possesses a different transmissivity for a surface plasmon polariton incident on it from one side of it than it has for a surface plasmon polariton incident on it from the opposite side. This asymmetric transmission of a surface plasmon polariton does not require either electrical nonlinearity or the presence of a magnetic field but is a consequence solely of the geometry of the structure. We have demonstrated that a system consisting of a square array of scatterers deposited on a metal surface in a triangular mesh to which a diffractive structure is added to the left side of it reveals asymmetric transmission when the frequency of the incident SPP is in the bandgap of the plasmonic crystal. The mechanism for this property is related to the higher Bragg modes that are excited due to the diffractive structure, while the 0-order beam, due to the existence of the band gap, is not transmitted through the structure. By varying the material and geometrical parameters of the diffractive structure one can control the contrast transmission that characterizes the degree of the asymmetry.