In this Letter, we demonstrate a way to make single-crystal LiNbO(3) optical fibers with silica glass cladding and In(2)O(3)-SnO (ITO) electrodes embedded between core and cladding with a one-step drawing process with the CO(2) laser-heated pedestal growth technique. A half-wave voltage (Vπ) of 6.6 V, effective electro-optic coefficient of 23.6 pm/V, and transmission loss of 0.89 dB/cm was achieved in the single-crystal LiNbO(3) optical fiber with core diameter of 9 μm and electrode distance of 50 μm. Furthermore, the technique can be applicable to make other single-crystal core optical fibers with ITO-embedded electrodes, which could potentially enable many electrically tunable fiber devices along with the unique property of the single-crystal core.