The objective of this paper was to design and analyze a dual wide band compact antenna for wireless application. Microstrip patch antenna limitation was overcome by using fractal geometry. The proposed antenna was designed with a radius of 15mm on a FR4 lossy substrate with relative permittivity of 4.4 and loss factor of 0.025. Measurement result showed that the antenna has a dual band of operation with bandwidth for return loss below -10dB of 1.84GHz (2.2GHz-4.07GHz) and 2GHz (6GHz-8GHz) which can be applied to wireless local area network (WLAN) and Ultra wide band applications.