A unique ‘ϵ’ shaped microstrip patch antenna with substrate ‘Rogers RT/duroid 5880(tm)’ has been investigated in this paper. The parametric study of the proposed structure is carried out using ANSOFT HFSS software. A dual frequency band response is obtained which is suitable for Wi-Max and WLAN applications. VSWR values of 1.0643and 1.1535 are obtained at the frequencies 2.2040GHz and 2.7780GHz respectively. High gain is also observed at both the frequencies. Besides the other characteristics were also studied with the help of smith chart and radiation pattern.