Inspired by the two-layer twisted graphene in electronics, Moire photonic lattices are also of great interest to researchers. Various Moire photonic configurations have been shown to possess peculiar photonic properties. In this paper, the photonic characteristics of Lieb Moire lattices composed of two overlapping Lieb sublattices with different rotation angles are studied. It is found that two Lieb sublattices can form a lattice with square characteristics when the rotation angle is 36.87°. Both the Lieb lattice and Lieb Moire lattice are composed of GaAs dielectric cylinders embedded in air. The radii of the cylinders of the two sublattices are r₂ and r₁ respectively. In order to compare their lattice properties, their lattice constants are set to be equal. With the same filling factor, the plane wave method is used to simulate the band structures of TM modes. According to numerical simulation, the Lieb Moire lattice has a wider photonic bandgap and a blueshift of the bandgap center than the conventional Lieb lattice, which is more suitable for optical communication applications. The main reason for the phenomenon is the change of dielectric contrast. To find the widest bandgaps, the filling factors of Lieb lattice and Lieb Moire lattice are further scanned, and the bandgap maps are obtained. The numerical simulation results show that the bandgap firstly increases and then decreases with the increasing filling factor, and the bandgap of Lieb Moire lattice is wider. At the same time, the photonic flat band properties are also observed. Three bands with very small gradients are observed in the band structure of Moire lattice, which are the 15th, 22nd and 27th bands. In order to indicate the characteristics of flat bands, the flatness is defined as F. Through calculation, the 22th band has the minimum F, meaning it has the highest flatness. By changing the size of the dielectric cylinders, the flatness of the flat band can be higher. The flat band can lead to localization of field near lattice. By calculating the intensity of electric field distribution at the Γ and K points in the 22th band with the highest flatness, it can be seen that the electric energies are obviously located tightly to the central rings of cylinders , which verifies the effective flatness of photon band. The flat band with higher flatness can lead to stronger localization of electric field, which has a wide application prospect in nonlinear optics, photoelectric energy conversion devices and so on. Changing the structural parameters and dielectric parameters of Lieb Moire lattice can further increase the width of bandgap. In order to obtain the optimized bandgap width, the materials are changed. The band characteristics of composite Moire Lieb lattice formed by the superposition of sublattices of different dielectric materials are also studied based on plane wave method. The dielectric material of the unrotated sublattice labelled as “A” was selected as GaAs, and the dielectric material of rotated sublattice labled as “B” was selected as SiO₂, and the superposition points of two sublattices were selected as GaAs. The dielectric cylinders are all embedded in air. It is proved that the composite Lieb Moire photonic lattice has a wider bandgap, which is mainly due to the reduced symmetry caused by the two kinds of materials. Then the radius relationship of the two sublattices is simply set as r₂=0.5r₁, and r₂ changes synchronously with r₁. The main bandgap width of the composite Lieb Moire photonic lattice is further increased, which can be attributed to the decrease in the overall lattice symmetry caused by the change of the radius. The Moire configuration based on Lieb lattice proposed in this paper provides a new method to improve the bandgap of photonic lattice, it provides a meaningful platform for studying the physical phenomena of flat band.