A previously unreported Pb-based perovskite PbMoO3 is obtained by high-pressure and high-temperature synthesis. This material crystallizes in the Pm3m cubic structure at room temperature, making it distinct from typical Pb-based perovskite oxides with a structural distortion. PbMoO3 exhibits a metallic behavior down to 0.1 K with an unusual T-sublinear dependence of the electrical resistivity. Moreover, a large specific heat is observed at low temperatures accompanied by a peak in CP/T3 around 10 K, in marked contrast to the isostructural metallic system SrMoO3. These transport and thermal properties for PbMoO3, 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 Pb2+ cations. We discuss the unusual behavior of the electrical resistivity in terms of a polaronlike conduction, mediated by the strong coupling between conduction electrons and optical phonons of the local low-energy vibrational mode.