This paper presents the design of a ultra-wideband monopole antenna based on fractal geometry. The proposed antenna is essentially composed of a hexagonal patch fed by a coplanar waveguide (CPW) Feed. To improve the characteristics of this antenna, trapezoidal shaped elements are added on his sides. This monopole fractal antenna is designed on RO4350B substrate having dielectric constant εr=3.66, loss tangent tan δ = 0.004 and thickness h=1.524 mm. The proposed antenna has compact size of 35×41×1.524 mm³ and exhibits a good return loss coefficient over the entire UWB frequency range from 3 GHz to 13 GHz.