A fractal log periodic antenna for a Ground Penetrating Radar (GPR) is designed and simulated to evaluate the detection of plastic mines. The Brewster pseudo-angle concept is considered in the simulation to force the reflection component to a minimum value. The methodology focuses on the characterization and modeling of the transmission media and the plastic mine, in addition, the presence of the standing wave in the system is simulated to evaluate the return signal in the receiving antenna of the GPR. As a result, the multiband characteristic of the log-periodic fractal antenna and the signal-to-noise ratio (SNR) of 10,17 dB obtained for the resonance frequency of 1,35 GHz stand out. Likewise, the pseudo-Brewster angle of 70,47° minimizes the reflection of the incident electromagnetic wave in the transition between two dielectric media, with losses and dispersive in frequency (free space-ground).