A high-extinction-ratio bandgap of air-bridge photonic crystal slab, in the near infrared, is reported. These structures were patterned in single-crystalline LiNbO3 film bonded to SiO2/LiNbO3 substrate by focused ion beam. To improve the vertical confinement of light, the SiO2 layer was removed by 3.6% HF acid. Compared with photonic crystals sandwiched between SiO2 and air, the structures suspending in air own a robust photonic bandgap and high transmission efficiency at valence band region. The measured results are in good agreement with numerically computed transmission spectra by finite-difference time-domain method. The air-bridge photonic crystal waveguides were formed by removing one line holes. We reveal experimentally the guiding characteristics and calculate the theoretical results for photonic crystal waveguides in LiNbO3 film.