This paper presents CPW -fed Square Shaped fractal antenna. The Antenna has been designed on FR4 substrate ??r = 4.3 and thickness 1.53 mm. The antenna has been fabricated and tested using VNA. The experimental result exibihits dual bands i.e. from frequency 0.79 GHz - 2.24 GHz and from frequency 3.53 GHz to 12.29 GHz. This corresponds to 1.45 GHz and 8.76 GHz respectively. The lower end frequency of antenna is shifted to 0.79 GHz in comparison to simple convention coaxially feed microstrip patch resonant 1.44 GHz. This reveals the size reduction of fractal antenna. The experimental radiation pattern of this antenna has been observed nearly similar at all frequencies. This type of antenna can be useful for GPS, PCS, Vehicular radar and imaging system applications.