The Coulomb pseudopotential ($\mu^*$), the important ingredient in the strong-coupling theory, is investigated in non-superconducting Pd and superconducting PdH using the density-functional approach with ab-initio pseudopotential. We first survey the structural properties and electronic structures of both materials, and calculate the full static dielectric matrices. The results indicate that the local field due to the localized 4d electrons significantly affects on the screening and therefore on the $\mu^*$. The calculated $\mu^*$ of Pd and PdH with the full many-body effect and local field effect is 0.153 and 0.104, respectively. The large $\mu^*$ of Pd compared with the assumed one in the McMillan``s $T_c$ equation attributes to the suppression of superconductivity. The $\mu^*$ of PdH represents the large decrease of the Coulomb interaction from that of pure Pd.