The Ground-penetrating radar (GPR) system is used for the detection of buried objects inside the earth and the classification of the subsurface structures. Ultra-wide band antenna is one of the major component of the GPR system; which is used to transmit and receive short pulse of electromagnetic nature. The performance of the GPR system in detecting buried object is mainly affected by the reflections of the GPR antenna. The reflections from the antennas itself is a basis of late-time ringing and distortion of antenna. These factors create problem in the identification of the objects. Several UWB antennas are used in the GPR system. This paper presents theoretical study for the design of ultra-wideband Bow-tie antenna as a GPR antenna. Bow-tie antenna is designed for a frequency range of 4-18 GHz. Transient and spectral behavior of the antenna is simulated. The time behavior of the antenna shows a reflected signal from the bow-tie antenna of the duration of 2.0 ns. The antenna provides a VSWR less than 2.0 and a return loss of less than -15 dB in the operating frequency range. Bow-tie antenna is then modeled and simulated in the GPR environments which includes the buried object (i.e. scatterer) and beam floor. The design, modeling and simulations are performed by using CST Microwave Studio.