The mechanical properties of metallic materials can be controlled by both alloy design and the construction of an appropriate structure. Porous materials are a promising candidate for bone-related devices because they have a low Young's modulus and allow bone ingrowth. Recently, great advancements have been made in additive manufacturing technology, also known as three-dimensional printing. This technology enables the arbitrary and independent control of the Young's modulus, strength of the material, the shape and volume fraction of the pores. Porous titanium samples composed of rhombicuboctahedron-derived units with sub-millimetre dimensions were fabricated by laser additive manufacturing, and the dependence of their mechanical properties on the structural parameters was investigated. Porous Ti samples with five different sets of dimensions were accurately fabricated as designed. The solid Ti parts of the samples were confirmed to contain no remarkable solidification voids by Archimedes' principle. The porosity can be easily controlled in the present structural design; the measured and designed porosities showed a good linear relationship, although the measured porosity was slightly larger than the designed porosity. The gradient of stress-strain curve in elastic region can be also arbitrarily controlled in porous Ti samples with the present structure; it increased as the minimum cross-sectional area ratio in the plane perpendicular to the loading axis increased. This means that Young's modulus can be arbitrarily controlled by the present structural control. However, it should be noted that the local mechanical properties such as Young's modulus of the fabricated samples are not uniform in the overall structures; to improve this, the effect of the structure on the retention and flow of heat must be considered.