This paper researches a novel 2D Z-shaped Electromagnetic Band-Gap (EBG) structure, its dispersion diagram and application field. Based on a transmission line model, the dispersion equation is derived and theoretically investigated. In order to validate theoretical results, a full wave analysis is performed and the electromagnetic properties of the structure are revealed. The theoretical results show good agreement with the full wave simulation results. The frequency response of the structure is compared to the well know structures of Jerusalem cross and patch EBG. The results show the applicability of the proposed 2D Z-shaped EBG in microstrip patch antennas, microstrip filters and high speed switching circuits, where the suppression of parasitic surface wave is required.