In the group of vanadium-free titanium alloys used for applications for long-term implants, the Ti-13Zr-13Nb alloy has recently been proposed. The production of a porous layer of oxide nanotubes (ONTs) with a wide range of geometries and lengths on the Ti-13Zr-13Nb alloy surface can increase its osteoinductive properties and enable intelligent drug delivery. This work concerns developing a method of electrochemical modification of the Ti-13Zr-13Nb alloy surface to obtain third-generation ONTs. The effect of the anodizing voltage on the microstructure and thickness of the obtained oxide layers was conducted in 1 M C2H6O2 + 4 wt% NH4F electrolyte in the voltage range 5–35 V for 120 min at room temperature. The obtained third-generation ONTs were characterized using SEM, EDS, SKP, and 2D roughness profiles methods. The preliminary assessment of corrosion resistance carried out in accelerated corrosion tests in the artificial atmosphere showed the high quality of the newly developed ONTs and the slight influence of neutral salt spray on their micromechanical properties.