An ultrafine-grained (UFG) microstructure in electron beam-melted casts of commercial pure niobium (Nb) was produced in an equal-channel angular pressing die with a right angle, without roundings, at 12 passes, and by the B (c) route. Additional microstructural improvements were made by hard cyclic viscoplastic deformation and the double-bounded microstructure was formed. The new nanoindentation technique was used to study the pure Nb micro-mechanical properties of the shear bands (SBs). The wear resistance of Nb was studied by a ball-on-plate tribometer with an alumina (Al2O3) counterface ball. The results showed that the nanohardness of pure Nb on boundaries of SBs was similar to 6 GPa, while inside of SBs, it was only similar to 3.5 GPa (measured under an indentation load of 10 mN). The corresponding elastic modules were similar to 150 and similar to 100 GPa, respectively. Such heterogeneity of the micromechanical properties has an influence on the coefficient of friction (COF) and the wear rate. The Nb with an UFG microstructure has an increased COF and a higher specific wear rate as compared to the as-cast sample. The COF depends on the direction of the wear test relative to the SBs' orientation. As the boundaries of SBs have the highest hardness, compared to areas inside of SBs, the wear track surface has a high roughness, which leads to an increase in the COF of the double-banded ultrafine-rained pure Nb.