In this paper the Fano resonance in a free-standing LiNbO(3) photonic crystal slab is demonstrated. We present a numerical analysis and experimental measurements with free space illumination where the dependence of slab thickness, radius of air holes and lattice types are investigated. The unique property of polarization dependence for LiNbO(3) photonic crystal slabs is also analyzed, and we show that the transmission spectra exhibit significant sensitivity (~25nm) to polarization. A monolithic free-standing LiNbO(3) photonic crystal slab was fabricated using ion beam enhanced etching (IBEE) technology. Measurement results of the reflection spectra agree with the numerical analysis.