Polarimetric synthetic aperture radar (SAR) is an effective technique to retrieve physical properties of planetary surfaces, such as the dielectric constant and surface roughness. Dielectric properties of lunar regolith are quite attractive for future lunar SAR missions. In this paper, we investigate the dielectric properties of lunar regolith by the Mini-RF SAR data. First, a new model of dielectric constant inversion for hybrid polarimetric SAR is proposed, in which the hybrid polarimetric scattering similarity parameter is first introduced. Second, the dielectric constants of Apollo 14, 16, 17 and Chang’E-5 landing sites are estimated through the proposed model. The inversion results fit well with the laboratory measurements of lunar samples, with an estimated root mean square error (RMSE) of 0.53. In addition, we analyze the dielectric properties of regolith on crater floors in different geologic settings, including the lunar maria, highlands, and permanently shadowed regions (PSRs) near the lunar poles. The results indicate that for craters with diameters of 5–25 km, the real part of the dielectric constant of regolith fines increases with crater depth-to-diameter (d/D) ratio, while no apparent correlation is found with crater diameter. Furthermore, the average dielectric constant of regolith fines is 3.01 in PSRs, which is less than that in the lunar maria and highlands (3.43 and 4.13, respectively). This implies that craters in PSRs may possess a looser regolith material compared to the mid-latitude craters. In a word, the proposed method is useful for estimating the dielectric properties of lunar regolith, and it is promising for future lunar SAR applications.