In the proposed paper a surface wave antenna is designed for millimeter wave application. We used a simple dipole structure whose length is optimized for millimeter wave (60 to 80 GHz) band. We introduced periodic patches with partial ground, which is responsible for guiding the surface wave along the partial ground and giving a directional radiation pattern as in case of monopole with reduction in magnitude of back lobe radiation. The proposed structure achieved a band width of ∼ 20 GHz (-10 dB), i.e., 60.5 to 80GHz. The maximum gain is around 8.32dBi at 64GHz and the average gain is of 7.5 dBi. The analyses of other antenna parameters like Co and cross polarization, gain, Radiation efficiency etc are also done.