With increasing demand of high speed wireless mobile applications, the mobile devices required to operate different real time applications like voice/video communication, Wi-Fi, GPS etc. All these applications requires different frequency bands for their operation, which call for multiband antennas. In this paper, Compact Monopole antenna has been proposed. The antenna has been designed with rectangular patch and fed by coaxial probe feed. Defected Ground Structure (DGS) etched on ground plane to improve the impedance matching of antenna. DGS provide bandwidth enhancement for antenna so the DGS is realized by the etching simple shape to complex shape and after analyzing the different DGS structure among arrow-head, H-Shape and Spiral shape the better result giving shape has been etched on ground plane to improve the performance of antenna. Further fractal geometry added on patch of antenna as known properties of fractals have no characteristic size, and are generally composed of many copies of themselves at different scales. These properties of fractal antennas lead to design new class of antenna with multiband and compact in size. The designed monopole antenna printed on FR4 substrate having thickness of 1.6 mm, relative dielectric constant of 4.4. The designed antenna has the properties of good performance, low side lobe levels, compact size and low cost. Effects of varying dimensions of patch of antenna and ground plane of antenna are observed on performance of antenna and design is optimized for better result. The stepwise design procedure is thoroughly discussed along with parametric analysis and tested for multiple applications. The designed Monopole antenna has return loss of less than 10 dB with bandwidth more than 350 MHz in the 2.4 GHz frequency band and more than 1.3 GHz in the 5.8-7 GHz frequency band. The Monopole antenna is simulated using the software IE3D (Integral Equation Three Dimensional) simulator and tested on Virtual Network Analyzer (VNA).