Many seismic data processing and inversion techniques have been applied to ground-penetrating radar ͑GPR͒ data without including the wave field attenuation caused by conductive ground. Neglecting this attenuation often reduces inversion resolution. This paper introduces a GPR inversion technique that accounts for the effects of attenuation. The inversion is formulated in the time domain with the synthetic GPR waveforms calculated by a finite-element method ͑FEM͒. The Jacobian matrix can be computed efficiently with the same FEM forward modeling procedure. Synthetic data tests show that the inversion can generate high-resolution subsurface velocity profiles even with data containing strong random noise. The inversion can resolve small objects not readily visible in the waveforms. Further, the inversion yields a dielectric constant that can help to determine the types of material filling underground cavities.