An optimized Vivaldi antenna is designed for lower band Ultra Wide Band (UWB) (0.5-1.5GHz) to be used in ground penetrating radar system. In order to increase the penetration depth and minimize the interference of the radiated signal, lower band of UWB is explored. An exponentially tapered slot Vivaldi antenna was designed and simulated using Ansoft HFSS. Parameters of the Vivaldi antenna were varied and simulation results were measured and compared. A directive radiation performance with a peak gain which is more than 9dB and return loss below -10dB in the desired band was achieved.