Uniform ultra-thin amorphous Nb films were able to be prepared by quench-condensation of Nb atoms on cold Al 2O 3 substrate of 10 ∼ 20 K in vacuum of ∼10 -10 torr. The onset of superconductivity has been studied by measuring the sheet resistances in situ down to 4 K and by changing the film thickness from ∼3 Å in a fine increasing step of ∼0.05 Å. As a film becomes thinner, the superconducting transition temperature becomes lower, compared with that of bulk Nb. Our amorphous Nb films exhibit superconductor-insulator transition at T=0 with the electric sheet resistance RN□ in the nomral state as a proper parameter for the transition. The threshhold RN□ is close to h/(2 e) 2, quantum resistance for electron pair. Thus, in amorphous superconducting thin films the onset of superconductivity will be universal.