A dual band linear polarized micro-strip antenna is designed and simulated to obtain electronic circuit miniaturization of an antenna in high speed wireless local area networks (IEEE 802.11a standard). The proposed antenna contains a substrate layer (FR-4 lossy) with a dielectric constant of 4.4 and there is a circular patch on the upper layer of the substrate. The coaxial probe feed is used to excite the desired antenna which reduces the spurious radiation and hence obtained good efficiency. It is shown that using cavity model 20% excess bandwidth can be achieved while maintaining the lower size of the antenna. An 'E' shaped slot is introduced in the radiating patch to obtain dual band resonance frequency with maximum current distribution on the surface. Finally the simulated results using Computer Simulation Technology (CST) microwave studio 2009 in this design is compared with manual computation results which are found to be suitable for WLAN applications.