By designing structures with different gradients, the strength of lattice structure can be improved, and its mechanical properties such as impact resistance, energy absorption and vibration reduction can be improved. The Voronoi method was used to generate random points in the Eulerian space domain to form the basic unit cell of lattice structure. The distribution forms of different gradient unit cell structure were set, and finally the lattice structures with different gradient were generated. In this experiment, “inward” gradient and “outward” gradient were designed, and five different lattice structures with gradient grades of 0.5, 0.6, 0.7, 0.8 and 0.9 were designed for “inward” and “outward” structures, respectively. And gradient level of the uniform lattice structure was 1.0. The finite element analysis software Abaqus was used to simulate the mechanical properties of lattice structures with different gradients. The lattice structures were fabricated by 3D printing technology, and the mechanical compression experiment was carried out to verify the finite element analysis results. The results of finite element analysis and experiments show that the mechanical properties of lattice structures with different gradients generated by Voronoi method are better than that of the uniform lattice structure; in the “inward” gradient lattice structures, the mechanical properties of the lattice structure with gradient grade 0.6 are the best, with good shock resistance and vibration reduction; in the “outward” gradient lattice structures, the mechanical properties of the lattice structure with gradient grade 0.8 is the best. The overall performance of “outward” gradient lattice structure is better than that of “inward” gradient lattice structure. The gradient lattice structures based on Voronoi method have good mechanical properties such as high strength, vibration resistance and energy absorption. The mechanical properties of lattice structures are closely related to the gradient grade.