We demonstrate the fabrication of single-mode optical waveguides on lithium niobate on an insulator (LNOI) by optical patterning combined with chemomechanical polishing. The fabricated LNOI waveguides had a nearly symmetric mode profile of ~2.5 µm mode field size (full-width at half-maximum). We developed a high-precision measurement approach by which single-mode waveguides were characterized to have propagation loss of ~0.042 dB/cm.