This work concerns the development of a method of functionalization of the surface of the biomedical Ti–6Al–7Nb alloy by producing oxide nanotubes (ONTs) with drug-eluting properties. Shaping of the morphology, microstructure, and thickness of the oxide layer was carried out by anodization in an aqueous solution of 1 M ethylene glycol with the addition of 0.2 M NH4F in the voltage range 5–100 V for 15–60 min at room temperature. The characterization of the physicochemical properties of the obtained ONTs was performed using SEM, XPS, and EDAX methods. ONTs have been shown to be composed mainly of TiO2, Al2O3, and Nb2O5. Single-walled ONTs with the largest specific surface area of 600 cm2 cm−2 can be obtained by anodization at 50 V for 60 min. The mechanism of ONT formation on the Ti–6Al–7Nb alloy was studied in detail. Gentamicin sulfate loaded into ONTs was studied using FTIR, TG, DTA, and DTG methods. Drug release kinetics was determined by UV–Vis spectrophotometry. The obtained ONTs can be proposed for use in modern implantology as carriers for drugs delivered locally in inflammatory conditions.