Abstract: The functional gradient design can effectively improve the mechanical properties and energy absorption performance of the structure. In order to investigate the mechanical response of triply periodic minimal surface structure with functional gradient thickness under static and dynamic loads and the influence of gradient wall thickness distribution on its mechanical properties, gyroid structures consisting of linear gradient and several nonlinear gradients (logarithmic gradient, sigmoid gradient and exponential gradient) are constructed. The structures are fabricated by 3D printing photosensitive resin and the quasi-static compression test is carried out. The numerical model is constructed by LS-DYNA and compared with the test results to verify the effectiveness of the numerical method. It is found that the functional gradient wall thickness distribution significantly affects the mechanical properties and deformation modes of the structures. Under quasi-static compression, the functionally graded structure presents a deformation mode of layer-by-layer collapse, and a local densification zone is generated at the contact end, which leads to a certain improvement in the energy absorption characteristics of the gradient structure. Based on quasi-static test and experimental deformation model analysis, the Gibson-Ashby model is constructed to reveal the variation of elastic modulus and yield strength of uniform structure with equivalent density. Using this Gibson-Ashby model, the yield strength of the functionally graded structure is predicted, and the iso-stress model is also constructed to predict the elastic modulus of the gradient structure. The predicted results are in good agreement with the experimental results. For the dynamic mechanical properties of the gradient structure, four kinds of impact velocity simulation models are constructed, and the influence of different impact velocities on the mechanical properties of the gradient structure is investigated. Under high-speed impact, the local collapse phenomenon of the functionally graded structure is more obvious due to the gradually increase thickness. As a result, the densification strain and energy absorption characteristics of the functionally graded structures are significantly increased under high-speed impact. Among them, the logarithmic gradient structure has the highest yield strength, while the sigmoid gradient structure has the highest average plateau stress and energy absorption characteristics, with a specific energy absorption characteristic of 13.01 J/g, which is 45% higher than the uniform structure with a relative density of 45%. In addition, the rigid-perfect plastic-locking model is used to predict the dynamic plateau stress of the gradient structure, and the fitting results are in good agreement with the simulation results, which provides a calculation method for predicting the dynamic mechanical response of the functional gradient structure.