Abstract Triply periodic minimal surface (TPMS) lattice structures are lightweight structures based on mathematical surfaces. They have been widely used in the field of additive manufacturing. In this study, single-morphology IWP and Diamond structures were designed using a parametric method. Based on the homogeneous structures, TPMS lattice structures with linear, cosine, and sinusoidal density gradients were further designed. Quasi-static compression experiments and numerical simulations were combined to systematically investigate the compressive deformation behavior, stress evolution, and energy absorption characteristics of the lattice structures under different topological configurations and density gradient distributions. The experimental and simulation results showed that all single-type structures exhibited a stress distribution with high stress at the upper and lower regions and low stress in the middle region. The Diamond structure showed better mechanical performance and energy absorption capability. It was more suitable for lightweight energy absorption applications. For the graded structures, the gradient stress of the IWP structures gradually decreased with decreasing density. In contrast, stress concentration was more likely to occur in low-density Diamond structures. Among all graded structures, the I-SIN structure showed the best overall performance. The D-COSINE structure exhibited the highest stiffness. The D-SIN structure demonstrated excellent load-bearing and energy absorption performance. For cylindrical configurations, the CY-D-SIN structure showed the best impact resistance. The overall performance of CY-Diamond structures was superior to that of CY-IWP structures. These structures can be adapted to different impact loading conditions.