A highly directive fractal antenna with a novel shape is proposed in this paper. Finite Element Method based simulations were carried out on the first three iterations of a hexagonal fractal ring and the performance was measured in terms of the resonant behavior, directivity, radiation efficiency, current distribution, and radiation pattern. The second iteration fractal antenna radiates well along the broadside direction at the fundamental mode of operation. The ground plane was modified to improve the performance further. The antenna, etched on an FR4 substrate, has a directivity of 11.8 dB along the broadside direction with multi-frequency broadband performance over the frequency range of 3.12-7.46 GHz. Therefore, the proposed fractal antenna can be used for Wireless LAN applications. The antenna was fabricated and measured in order to validate the results.