We report a new type of all-Nb tunnel junction and single electron transistor (SET) fabricated using conventional electron-beam lithography and angle evaporation combined with an ion beam oxidation technique to create a tunnel barrier between the Nb electrodes. Significantly improved reproducibility in fabrication is achieved compared with previous Nb/Al-AlOx/Nb structures. The basic parameters of the Nb/NbOx/Nb junctions, namely, the barrier height and width, are extracted from the temperature-dependent current-voltage characteristics. The transport characteristics of various all-Nb superconducting SETs with different tunnel barriers are presented and discussed. Clear gap features are observed, and a corresponding gap energy (DeltaNb) of up to 1.1 meV is obtained. From the transport characteristics of the Nb-based SET measured at sim40 mK in the normal state, we estimate the specific junction capacitance to be sim440 pm 50 fF/mum2. We also discuss how the quality ({it i.e.}, Tc) of the Nb stripes is affected by outgassing from the various resists used in the fabrication.