In the current scenario small, compatible and affordable microstrip patch antennas are developed in wireless communication industries keep on improving antenna performance.One of important concept to design antenna is that antenna have small size. For WLAN and WI-MAX applications, one may want that antenna must have small size and must be capable to resonate at multiple frequency bands. There are number of techniques that can be useful for designing of antenna which include making use of fractal geometry, use of slot and DGS. In this research work, I shape along with Z shape slots are inserted on the patch. The dimension of ground and path that are considered in this research work are 32.6mm×27.6mm and 18mm×23mm respectively. Then the performance parameters like gain, return loss, Bandwidth, radiation pattern and NSWR are measured for simple as well as for DGS antenna. The substrate used for the proposed antenna is FR4 with relative permittivity 4.4 and loss tangent is 0.02. The simulation is carried out in HFSS software. At lat the comparison of proposed with existing work is provided.