In order to obtain a lightweight, high-strength, and customizable cellular structure to meet the needs of modern production and life, the mechanical properties of four thickness gradient honeycomb structures were studied. In this paper, four types of honeycomb structure specimens with the same porosity and different Poisson’s ratios were designed and manufactured by using SLA 3D-printing technology, including the honeycomb, square honeycomb, quasi-square honeycomb, and re-entrant honeycomb structures. Based on the plane compression mechanical properties and failure mode analysis of these specimens, the thickness gradient is applied to the honeycomb structure, and four structural forms of the thickness gradient honeycomb structure are formed. The experimental results show that the thickness gradient honeycomb structure exhibits better mechanical properties than the honeycomb structure with a uniform cellular wall thickness. In the studied thickness gradient honeycomb structure, the mechanical properties of the whole structure can be significantly improved by increasing the thickness of cell walls at the upper and lower ends of the structure. The wall thickness, arrangement order, shape, and Poisson’s ratio of the cell all have a significant impact on the mechanical properties of the specimens. These results provide an effective basis for the design and application of cellular structures in the future.