Ultra-wideband (UWB) pulse radar has high range resolution and permeability in a dielectric medium, and has great potential for the non-destructive inspection or early-stage detection of breast cancer. As an accurate and high-resolution imaging method for targets embedded in a dielectric medium, extended range points migration (RPM) has been developed. Although this method offers an accurate internal target image in a homogeneous media, it assumes the permittivity of the dielectric medium is given, which is not practical for general applications. Although there are various permittivity estimation methods, they have essential problems that are not suitable for clear, dielectric boundaries like walls, or is not applicable to an unknown and arbitrary shape of dielectric medium. To overcome the above drawbacks, we newly propose a permittivity estimation method suitable for various shapes of dielectric media with a clear boundary, where the dielectric boundary points and their normal vectors are accurately determined by the original RPM method. In addition, our method iteratively compensates for the scattered waveform deformation using a finite-difference time domain (FDTD) method to enhance the accuracy of the permittivity estimation. Results from a numerical simulation demonstrate that our method achieves accurate permittivity estimation even for a dielectric medium of wavelength size.