A single layer substrate compact dual band rectangular micro-strip patch antenna with transmission line feeding is designed for Wireless Local Area Networks (WLAN) implementation. The desired antenna consists of a rectangular patch having two I-slots and a dielectric material with dielectric constant of 2.4. The use of cavity model with transmission line feed has the favor of low profile, high gain and wide bandwidth of the antenna. The antenna has overall size of 46.9 mm by 38.01 mm and gives bandwidth of about 90 MHz at resonance frequency of 2.45 GHz and that of 115 MHz at 4.1 GHz frequency with Defected Ground Structure (DGS). The antenna with DGS has return losses -21.25 dB at 2.45 GHz and -27.5 dB at 4.1 GHz where the gains are 6.70 dB for 2.45 GHz and 6.80 dB for 4.1 GHz. Finally the designed antenna has been simulated using Computer Simulation Technology (CST) microwave studio 2009 and it is comparable with manual computation results which are found to be suitable for WLAN applications.