Full waveform inversion (FWI) is an advanced inversion technique for ground penetrating radar (GPR), which could provide quantitative, high-resolution subsurface imaging. FWI has been used widely to process crosshole and on-ground multi-offset GPR data, but its application to on-ground common-offset GPR data is more difficult and being developed. This is mainly because that on-ground common-offset GPR has much less coverage of the subsurface and mainly includes reflective information. The application of conventional FWI to pure reflection data in the absence of a highly accurate starting velocity model is difficult. Here, we demonstrate a means of achieving this successfully by preprocessing the observed data and the residual fields with an integral algorithm, which could produce a more reasonable gradient and therefore lead to better inversion results. Several cases verify the effectiveness of this method. We achieve the simultaneous inversion of relative permittivity and conductivity for on-ground common-offset GPR, and discuss the trade-off between permittivity and conductivity in details. According to the inversion results of test models, it seems that the inversion result of relative permittivity is more credible in most cases.