The static and dynamic properties of the honeycomb non-pneumatic tires (NPTs) are strongly influenced by the spoke structure. Due to the complexity of the honeycomb structure, an in-depth understanding of the influences of the design parameters related to the honeycomb structure on its mechanical properties is essential, particularly for designing NPT of desired properties. Inspired by the concept of functionally graded structure, this paper aims to design a novel non-pneumatic tire with honeycomb-spoke graded thickness. Firstly, the in-plane mechanical characteristics of the thickness-graded honeycomb structures were investigated theoretically. On this basis, the finite element technique was developed for the NPTs using the corresponding thickness-graded honeycomb structures were established, and their static and dynamic mechanical properties were investigated using simulations and experimental tests. The results show that a reasonable thickness design can effectively enhance the load-bearing capacity of the NPT. The deformation features of the spoke were analyzed under the static state, and the contribution of different honeycomb structure edges deformation on the spokes is also discussed. The stress of the spoke and the tread under the static and dynamic loading conditions were studied, and comparison with the NPT-4 with a uniform thickness honeycomb structure, the results show that the thickness-graded honeycomb structure in NPT-3 significantly amplifies its load-bearing capability while also providing effective cushioning and shock absorption properties. This work would provide a basis for innovative design and performance optimization of NPTs.