A novel cellular structure is proposed based on bionic structure with negative Poisson's ratio characteristic, and the cell is periodically expanded in the in-plane direction to create a new honeycomb structure. The influence of gradient changes of the structural parameters on the load-bearing capacity and damping characteristics of the structure is investigated through a combination method of finite element numerical simulations and experiments. The results indicate that the concentric gradient arrangement of cell wall thickness and angle parameters, and the symmetrical gradient arrangement of cell height, wall thickness and angle parameters have the most significant influence on the static bearing capacity of the structure. In contrast, the gradient arrangement under the corner circle diameter has minimal effect on the static bearing capacity of the structure. Under the same conditions, the peak values of the transmissibility of C2 (large angle at constraint end and loading end, and smaller angle in the middle) and C3 structures (angle gradually increases from the loading end to the constraint end) are significantly reduced between the frequency 2 Hz and 1024 Hz. The peak values of the transmissibility of the structures C2 and C3 are respectively decreased by 20% and 25% compared to that of the non-gradient structure. This shows that the vibration damping effect of these two structures is better. The structure with the gradient change and the structure without the gradient change of the new honeycomb structure can both achieve certain vibration reduction and isolation from the middle to high frequency range.