Evaluating wide-band performance of ground-penetrating radar (GPR) antennas is a challenging task due to the complex electromagnetic coupling effects between the GPR antennas and the platform. Typically, the efficiency of conventional methods utilized to deal with the problem is quite low. However, there are various frequency sweeping techniques which can achieve fast analysis of antennas over a broadband. Accordingly, this paper describes an efficient hybrid scheme, based upon the electric field integral equation (EFIE), for modeling a GPR antenna which is mounted on an electrically large platform. In this paper, an antenna with two half-elliptical-shape arms, which is an improvement of bowtie antennas, is presented with resistances loaded in the terminal. A shallow rectangular conducting backed cavity is attached to the antenna. On the other hand, the best uniform rational ap- proximation technique is applied to analyze the wide-band property of the antenna since it can avoid repeatedly solving the integral equation at each single frequency point. The main scheme of the frequency sweeping method is as follows: 1) determining the Chebyshev nodes within a given frequency range; 2) computing the equivalent surface currents of antennas at the frequency points corresponding to those Chebyshev nodes; 3) calculating the wide-band response of surface currents according to the Chebyshev series. Finally, the Maehly approximation is utilized to improve the accuracy by matching the Chebyshev series to a rational function. In the hybrid scheme, the adaptive integral method (AIM) is applied to accelerate matrix-vector products as the IE algorithm and the impedance matrix is stored in a sparse form to facilitate analysis of large antenna-platform system. It is easy to combine the best uniform rational approx- imation technique with AIM but also other IE methods which are suited for modeling radiation of antennas. This hybrid method greatly extends the range of conventional numerical modeling for GPR antenna system. Furthermore, the efficiency and capability of the presented algorithm can be validated by the designed GPR antenna.