  A previously unreported Pb-based perovskite PbMoO$_3$ is obtained by
high-pressure and high-temperature synthesis. This material crystallizes in the
$Pm\bar{3}m$ 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.
