A new form of modified CPW-fed half circle fractal patch antenna is proposed for dual band 2.4/5.2 GHz Wireless Local Area Network (WLAN) application. The circular shape antenna based on the Descartes Circle (DC) theorem and iteration of self similar design. The-10 dB return loss (VSWR 2:1) impedance bandwidth in 2.4 GHz band is 28% and it covers the required bandwidth for 2.4 GHz WLAN. The 5.2 GHz resonant mode has impedance bandwidth of 40% covering 5.2/5.5/5.8 GHz WLAN bands. The EM characteristics of the antenna are presented by the current distribution. Proposed antenna maintained good radiation patterns with gain. Detailed design steps and results for the designs are studied and investigated in this paper. © 2011 IEEE.