Future wireless communication needs antenna with multifunctional operation. This paper focuses on Terahertz Antenna that could be easily integrated with micro and nano devices. In this paper, an octagonal shaped Microstrip Fractal Antenna loaded with the EBG structure is designed for tri-band terahertz application. Triple band characteristic achieved by fractal radiating patch is loaded with Electronic Band Gap (EBG). The antenna is working on triple band characteristics at 948 GHz, 984GHz and, 1040 GHz with overall dimensions of 700x900 µm2. The result and performance show that the recommended antenna will be compatible with compact wireless devices and Monolithic Microwave Integrated Circuit (MMIC). All simulation work has been done using electromagnetic software Ansoft High Frequency Structure Simulator (HFSS) and CST studio suite. The electromagnetic features like S11 parameters, VSWR, gain, efficiency and the radiation characteristics of such antenna are also explored. The simulation results show that this antenna has 9 dB realized gain at 0.948 THz resonating frequency.