Compared with traditional inorganic ferroelectric materials, organic molecular ferroelectric materials possess many advantages, such as light weight, flexibility, no heavy metal atoms and low cost, and have received extensive attention for a long time. In recent years, atomic-thick two-dimensional (2D) inorganic ferroelectric materials have achieved breakthrough and attracted much attention. However, there are few reports on the design and research of two-dimensional organic ferroelectric materials. In this paper, we theoretically propose a 2D monolayer organic ferroelectric molecular crystal with the cyclobutene-1,2-dicarboxylic acid (CBDC) molecules as the building block based on density functional theory calculations. The bulk of CBDC molecular crystals clearly shows layered structure due to the chain-like arrangement of hydrogen bonds in crystal. It is found that the internal hydrogen bond chains give rise to the anisotropic cleavage energy values along different crystal planes of the CBDC molecular crystal bulk. Theoretical calculation suggests that the CBDC based 2D monolayer organic ferroelectric molecular crystal can be achieved by the mechanical/chemical peeling along the (102) crystal plane because of the lowest cleavage energy. It is predicted that the in-plane spontaneous polarization of the CBDC (102) molecular crystal monolayer is ～0.39 × 10^–6 μC/cm, which is comparable to those of some inorganic counterparts. Calculations also indicate that the CBDC (102) molecular crystal monolayer shows a high polarization reversal barrier and is sensitive to the external uniaxial stress. The CBDC (102) monolayer organic ferroelectric molecular crystal reveals high in-plane spontaneous polarization with polarization reversal barrier easily modulated by the interface strain engineering, thereby rendering it great potential in lightweight, metal-free and flexible ferroelectric devices.