This paper presents comparative study of a rectangular Microstrip patch antenna at Terahertz (THz) frequency ranging from 0.6 to 1 THz with and without superstrate. The results report ed here were obtained using Ansoft HFSS 11.0 which uses full wave finite element method for simulation. In this study the miniature antenna was simulated first and then we load it with a superstrate and varied the height of the superstrate to optimize the antenna performance. Here in this paper we have selected 4 antenna configurations to compare. First antenna is a simple rectangular patch, second antenna is having a superstrate of height 50 microns, Third antenna is with a superstrate of 75 micron height and the fourth antenna is with a superstrate of 100 micron. Best performance of antenna i.e., -10dB bandwidth of around 19% was achieved at central frequency of 0.5 THz and 75 micron superstrate height.