Ground-penetrating radar (GPR) is a widely used tool for the detection and location of buried utilities. Buried pipes generate characteristic diffraction hyperbolas in raw GPR data. Current methods for analyzing the shapes and timing of the diffraction hyperbolas are very effective for locating pipes, but they are less effective for determining the diameter of the pipes, particularly when the pipes are smaller than the radar wavelengths, typically a few tens of centimeters. A full-waveform inversion (FWI) method is described for improving estimates of the diameter of a pipe and confirming the infilling material (air/water/etc.) for the simple case of an isolated diffraction hyperbola on a profile run perpendicular to a pipe with antennas in broadside mode (parallel to the pipe). The technique described here can improve a good initial guess of the pipe diameter (within 30%–50% of the true value) to a better estimate (less than approximately 8% misfit). This method is developed by combining two freely available software packages with a deconvolution method for GPR effective source wavelet estimation. The FWI process is run with the PEST algorithm (model-independent parameter estimation and uncertainty analysis). PEST iteratively calls the gprMax software package for forward modeling of the GPR signal as the model for the pipe and surrounding soil is refined.