A previously unreported Pb-based perovskite PbMoO$_3$ is obtained by high-pressure and high-temperature synthesis. This material crystallizes in the $Pmbar{3}m$ cubic structure at room temperature, making it distinct from typical Pb-based perovskite oxides with a structural distortion. PbMoO$_3$ exhibits a metallic behavior down to 0.1 K with an unusual $T$-sub linear dependence of the electrical resistivity. Moreover, a large specific heat is observed at low temperatures accompanied by a peak in $C_P/T^3$ around 10 K, in marked contrast to the isostructural metallic system SrMoO$_3$. These transport and thermal properties for PbMoO$_3$, taking into account anomalously large Pb atomic displacements detected through diffraction experiments, are attributed to a low-energy vibrational mode, associated with incoherent off-centering of lone pair Pb$^{2+}$ cations. We discuss the unusual behavior of the electrical resistivity in terms of a polaron-like conduction, mediated by the strong coupling between conduction electrons and optical phonons of the local low-energy vibrational mode.
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