Fractal geometry involves a recursive generating methodology those results in the figure with infinitely convoluted fine structures. They do not use additional loading components and are simple and cost-effective to fabricate. They can be mounted to constraining form factors, such as the casing of hand-held transceivers. In this paper, a fractal antenna is designed with Square and Hexagonal shape and operating between 4-7 GHz. The proposed antenna with the rectangular ground plane is modeled and simulated with Finite Element Method (FEM) based High-Frequency Structure Simulator (HFSS) and an improvement in performance parameters (Return loss, Bandwidth (BW) and VSWR) is observed with change in design parameters. Fractal antennas prove worthwhile, high performance, resonant antennas for many practical applications. It is usually fabricated as or on small circuit boards, they allow new versatility in their use with wireless devices.