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A dual-band design of a finite ground coplanar waveguide (CPW) fed antenna is presented for simultaneously wireless local area network (WLAN) and worldwide interoperability for Microwave Access (WiMAX) applications. The proposed antenna, comprising a rectangular planar patch element embedded with two L shaped slots. The simulated -10 dBi bandwidth for return loss is from 2 to 6 GHz, covering some of the WiMAX and WLAN bands. The parametric study is performed to understand the characteristics of the proposed antenna. Also, good antenna performances such as radiation patterns and antenna gains over the operating bands have been observed and simulated peak gain of the antenna is 7.68 dBi at 2.8 GHz and maximum return loss is obtained is -35 dBi at 4.8GHz.