For a typical marine shale reservoir in the Jiaoshiba area, Sichuan Basin of China, P-impedance is sensitive for identifying lithology but not suitable for indicating good shale reservoirs. In comparison, density is an important quantity, which is sensitive for identifying the organic-rich mud shale from non-organic-rich mud shale. Due to the poor data quality and incidence angle range, density cannot be easily inverted by directly solving the ill-posed pre-stack seismic inversion in this area. Meanwhile, the traditional density regularizations implemented by directly using the more robust P-impedance inversion tend to be inaccurate for recovering density for this shale reservoir. In this paper, we combine the P-impedance and the minus uranium to construct the pseudo-P-impedance (PIp) at well locations. The PIp is observed to be sensitive for identifying organic-rich mud shale and has a good correlation with density in this area. We employ the PIp-density relation into the pre-stack inversion framework to estimate density. Three types of regularization are tested on both numerical and field data: These are no regularization, traditional regularization and the proposed approach. It is observed that the proposed method is better for recovering the density of organic-rich mud shale in the Jiaoshiba area.