This paper describes the design and simulation of a compact CPW fed graphene patch antenna with Z shape slot. Antenna design is enhanced by the introduction of a ‘Z’ shaped slot in the patch of the antenna, that make it compact. Antenna resonates at the frequency of 2.4 GHz, for Wi-Fi uses. Polyamide Kapton tape of thickness 100µm and relative permittivity of 3.5 is used as the substrate. Graphene is used to make the conducting patch, feed and grounds of the antenna design. Various antenna parameters including reflection coefficient, radiation patterns and surface currents and parametric study of a physical parameter related to antenna design are discussed. The proposed antenna is ~20% smaller than the patch antenna at the same resonance frequency.