The tribological properties of a novel porous Ti–Nb–Ta–Fe–Mn alloy with 0%, 30%, and 60% porosity were evaluated for biomedical applications. The tribotesting was performed using a ball-on-disc under dry conditions, using an alumina ball and 1 N of a load. The coefficient of friction at the early stage of the porous samples was lower than that of the bulk, 0.2 and 0.7, respectively, but the samples with 30% porosity shift toward the bulk value after a variable number of cycles, while the samples with 60% remained stable after 100,000 cycles. The wear rate of the specimen with 60% porosity was twice as low as that of the bulk. The results are explained by shift in wear mechanism associated with the modified bearing ratio of the porous surface and by the accumulation of wear debris inside the pores, which prevented the development of three-body abrasion.