In this thesis, the study focuses on the tunable frequency ratio of Sierpinski Gasket fractal antennas and we use the SAW substrate of piezoelectric material. By using the fractal structure and the substrate of piezoelectric material, the goal of the miniaturized antenna is achieved. The proposed antenna can be widely used in wireless communication products. Firstly, we design the Sierpinski Gasket fractal antenna on the FR4 substrate. The asymmetric geometry of Sierpinski Gasket fractal structure is proposed and we choose the proper discontinuity locations to design the three-band and tunable antenna for IEEE 802.11b/g/a wireless communication systems. The preliminary design of the Sierpinski Gasket fractal structure on the piezoelectric substrate allows us to compare simulated and measured results to improve the non-ideal processing factors. Finally, comparing with the existing products, we reduce the size of the miniaturized fractal antenna to 5x5mm^2 on the SAW substrate by coplanar waveguide, coupled-fed, shorting with conductive adhesive and high iteration stage of half-Sierpinski Gasket fractal structure for GPS band and IEEE 802.11b/g applications.