In this paper, a rectangular eight shaped Electromagnetic Band Gap (EBG) structure at 5.8 GHz Industrial, Scientific and Medical (ISM) band for wearable application is proposed with intent to improve impedance bandwidth of antenna. The unit cell of an EBG structure is formed using eight shape on outer ring with inner square patches. The simulation of the eight shape EBG unit cell is carried out using eigen mode solution of Ansys High Frequency Structure Simulator (HFSS). Simulated results are validated by experimental results. The application of proposed EBG for an inverse E-shape monopole antenna at 5.8 GHz is also demonstrated. Band stop property of EBG structure reduces surface waves, and therefore, the back lobe of a wearable antenna is reduced. The frequency detuning of antenna takes place due to high losses in human body. Suitably designed EBG structure reduces this undesirable effect and also improves front to back ratio. The proposed compact antenna with designed EBG has observed the impedance bandwidth of 5.60 GHz to 6.15 GHz which covers 5.8 GHz ISM band. Evaluation of antenna performance under bending condition and on-body condition is carried out. Effectiveness of EBG array structure for Specific Absorption Rate (SAR) reduction on three layer body model is demonstrated by simulations. Calculated values of SAR for tissue in 1 g and 10 g are both less than the limitations. In conclusion, it is appropriate to use the proposed antenna in wearable applications.