Abstract: The mathematical model of surface area and its surface curvature was established, and the relationship between the least action principle and the minimal surface was discussed. The minimal surface lattice structures in the body-centered cubic (BCC) configuration with volume fraction of 20% and 30% were designed. The minimal surface lattice structures and traditional lattice structures were formed by laser selective melting with Ti-6Al-4V alloy powder as raw materials. The influence of the least action principle on the surface area, curvature characteristics and mechanical properties of lattice structures was studied, and the minimal surface lattice structure in the cross-cube configuration was used for further verification. The results show that the mean curvature of minimal surface was zero, following the least action principle. In the BCC configuration, compared with the traditional lattice structures, the surface curvature distribution of the minimal surface lattice structures was more concentrated. When the volume fraction was 20% and 30%, the surface area of the minimal surface lattice structure was reduced, and the stiffness and the energy absorption and elastic limit during elastic deformation increased. In the cross-cube configuration, compared with the traditional lattice structure, the surface area of the minimal surface lattice structure was reduced and the modulus of elastic increased. Compared with the traditional lattice structure in the same topological configuration, the mechanical properties of the minimal surface lattice structure were better; that was because the minimal surface followed the least action principle, having smaller surface area and more concentrated surface curvature distribution, resulting in alleviation of stress concentration at the nodes.