Pb nanobridges with a thickness of less than 10 nm and a width of several hundred nm have been fabricated from single-crystalline Pb films using low-temperature molecular beam epitaxy and focus ion beam microfabrication techniques. We observed novel magnetoresistance oscillations below the superconducting transition temperature (T_C) of the bridges. The oscillations—which were not seen in the crystalline Pb films—may originate from the inhomogeneity of superconductivity induced by the applied magnetic fields on approaching the normal state, or the degradation of film quality by thermal evolution.