Ultra-wide band (UWB) pulse radar with high range resolution and dielectric permeability is promising as an internal imaging technique for non-destructive testing or breast cancer detection. Various imaging algorithms for buried objects within a dielectric medium have been proposed, such as aperture synthesis, the time reversal approach and the space-time beamforming algorithm. However, these algorithms mostly require a priori knowledge of the dielectric medium boundary in image focusing, and often suffer from inadequate accuracy to identify the detailed structure of buried targets, such as an edge or specular surface owing to employing the waveform focusing scheme. To overcome these difficulties, this paper proposes an accurate and non-parametric (i.e. using an arbitrary shape without target modeling) imaging algorithm for targets buried in a homogeneous dielectric medium by advancing the RPM (Range Points Migration) algorithm to internal imaging issues, which has been demonstrated to provide an accurate image even for complex-shaped objects in free-space measurement. Numerical simulations, including those for two-dimensional (2-D) and three-dimensional (3-D) cases, verify that the proposed algorithm enhances the imaging accuracy by less than 1/10 of the wavelength and significantly reduces the computational cost by specifying boundary extraction compared with the conventional SAR-based algorithm.