In this paper, a structure of a patch antenna operating at 0.5 GHz is proposed for ground-penetrating radar (GPR) applications, with an optimized performance at low frequencies. The structure was designed using FR4 substrate, with a 4.4 permittivity value, and a tangent loss equivalent to 0.021. The prototype design is backed by an optimized rectangular reflector, which has improved the antenna gain and directivity. The performance of the antenna is evaluated in terms of the return loss, gain, and the radiation pattern for two cases, with and without a reflector. When using the reflector, a good radiation pattern is obtained, a wide operational bandwidth ranging from 0.4GHz and 1.25 GHz is achieved, and an increased gain from 4.3 to 7.43dB was realized.