Lightweight and strong lattice materials are suitable for a wide range of applications in aerospace, automotive, biomedical, shipbuilding, and a variety of other significant industries. A class of mathematically defined surfaces that exhibit three-dimensional (3D) periodicity, zero mean curvature, and large surface area is the triply periodic minimal surface (TPMS). Inspired by natural systems, such as biological cubic membranes, sea urchins, and butterfly wing scales, TPMS lattice material is composed of continuous and smooth shells, allowing for decreased stress concentration by comparison with strutbased lattice material. In this study, strut-based lattice materials, namely octet-truss (O) and tetrakaidecahedral (T), shell-based lattice materials, namely Diamond (D); Gyroid (G); and I-WP (I), and Primitive (P) lattice materials, were rationally designed and manufactured using Ti-6Al-4V alloy powder by selective electron beam melting (SEBM) process. The discrepancies between the design and manufactured diameters or thicknesses, optical microstructures, and mechanical properties of these lattice materials have been defined in detail. The results showed that the variations between the design and manufactured diameter or thickness of SEBM manufactured lattice materials were smaller than the value of the electron beam spot diameter, showing good geometric consistency with the original computer-aided design models. Due to the high thermal gradients and rapid cooling rates observed in the SEBM process, the resulting microstructure of lattice materials was columnar prior beta grains, which were parallel to the build direction, where inside the columnar beta grains were alpha + beta and martensite alpha' platelets. The key finding is that TPMS lattice materials exhibit superior mechanical properties compared to strut-based lattice materials in compressive strength, elastic modulus, and plasticity, owning to their smooth and continuous surface. Among the SEBM manufactured shell-based lattice materials, the mechanical properties of type D lattice materials perform best. Moreover, the specific compressive strength of SEBM manufactured shell-based lattice materials reached 146.9 MPa/(g.cm(-3)), which is much higher than that of strut-based lattice materials with 119.6 MPa/(g.cm(-3)) in the same relative density. These properties make TPMS or shell-based lattice materials potential candidates to be applied as parts in aerospace and/or biomedical industries.