  By partially doping Pb to effectively suppress the superstructure in
single-layered cuprate Bi2Sr2CuO6+{\delta}(Pb-Bi2201) and annealing them in
vacuum or in high pressure oxygen atmosphere, a series of high quality
Pb-Bi2201 single crystals are obtained with Tc covering from 17 K to
non-supercondcuting in the overdoped region. High resolution angle resolved
photoemission spectroscopy (ARPES) measurements are carried out on these
samples to investigate the evolution of the Fermi surface topology with doping
in the normal state. Clear and complete Fermi surface are observed and
quantitatively analyzed in all these overdoped Pb-Bi2201 samples. A Lifshitz
transition from hole-like Fermi surface to electron like Fermi surface with
increasing doping is observed at a doping level of ~0.35. This transition
coincides with the change that the sample undergoes from superconducting to
non-superconducting states. Our results reveal the emergence of an
electron-like Fermi surface and the existence of a Lifshitz transition in
heavily overdoped Bi2201 samples. They provide important information in
understanding the connection between the disappearance of superconductivity and
the Lifshitz transition in the overdoped region.
