This paper describes the design and simulation of compact dual band microstrip patch antennas: (1) Singleslotted rectangular microstrip antenna (RMSA) with ground slot. (2) Minkowski fractal microstrip patch antenna, using IE3D electromagnetic simulation software. The rectangular microstrip patch antenna is realised by single slotted single band rectangular microstrip antennas having slot in the ground plane. The open ended slot in the antenna generate wide impedance band which is shifted to lower frequencies by the effect of slot in the ground plane. The length and position of each slot is altered to operate the antenna in IEEE 802.11a WLAN frequency (5.15-5.35 and 5.725-5.825GHZ). Minkowski fractal microstrip patch antenna based on minkowski curve is advantageous due to their multiple resonating capabilities or enhancing the bandwidth. The performance characteristic of the fractal antenna is studied at four different stages to meet the frequency requirement for GSM and GPRS systems, C-band and wide band applications.