The properties of the guided modes, including the single-mode conditions and the coupling of different polarized modes in the single-crystal lithium niobate photonic wires, were analyzed in detail. One-dimensional photonic crystal micro-cavities with several different patterns, which could be used as an ultra-compact optical filter, were designed and simulated in order to get high transmission at the resonant wavelength and the best preferment. The designed structure, with the whole size of 6.5 × 0.7 μm2, was fabricated on a single-mode photonic wire. A measured peak transmission of 0.34 at 1400 nm, an extinction ratio of 12.5 dB and a Q factor of 156 were obtained. The measured transmission spectrum was basically consistent with the simulation, although a slight shift of resonant wavelength occurred due to the fabrication errors.