The design of novel biomimetic bone tissue scaffolds (BTS) using computer aided design (CAD) technology is challenging additive manufacturing technologies. At the microstructure level, BTS should mimic bone histomorphometry and assure optimum mass transport and mechanical properties. In this study, a novel BTS has been designed, by using a parametric and variational CAD method, to model a bio-inspired and interconnected porous structure. The mechanical (elastic modulus) and the fluid mass transport (permeability) properties have been computed and compared to other implicit surfaces modelling scaffolds. The results showed that the new BTS could be tuned during the design stage to match the microstructure and the histomorphometry properties of trabecular bone. Those with porosities between 0.7 and 0.9 and highly smooth curvatures were the most appropriates. The new BTS, once appropriately designed, could be made/manufactured by 3D printing technology with an internal microstructure mimicking the local bone properties of the selected bone volumes of interest, for example, those coming from computed tomography medical images.