In this report, we present an investigation of the optical properties and band structure calculations for the photonic crystal structures (PCs) based on one-dimensional (1D) and two-dimensional (2D) ferroelectric LiNbO3 crystal. Here we use 1D and 2D periodic crystal structure of dielectric rods and layers in air background. We have theoretically calculated photonic band structure and optical properties of 1D and 2D LiNbO3 PCs. Beside, we have calculated affect PBG properties of different parameters such as filling fraction and the shape. In order to get photonic gap map, we have calculated the gaps as a function of radius of the rods. We have also investigated the nature of guided modes in line defect waveguide. In our simulation, we employed the finite-difference time domain (FDTD) technique which implies the solution of Maxwell equations with centered finite-difference expressions for the space and time derivatives. © 2013 IEEE.