Bio-inspired porous metallic scaffolds have tremendous potential to be used as artificial bone substitutes. In this work, a radially graded lattice structure (RGLS), which mimics the structures of natural human bones, was designed and processed by laser powder bed fusion of martensitic Ti-rich TiNi powder. The asymmetric tension-compression behaviour, where the compressive strength is significantly higher than the tensile strength, is observed in this Ti-rich TiNi material, which echoes the mechanical behaviour of bones. The morphologies, mechanical properties, deformation behaviour, and biological compatibility of RGLS samples were characterised and compared with those in the uniform lattice structure. Both the uniform and RGLS samples achieve a relative density higher than 99%. The graded porosities and pore sizes in the RGLS range from 40%-80% and 330-805 μm, respectively, from the centre to the edge. The chemical etching has significantly removed the harmful partially-melted residual powder particles on the lattice struts. The compressive yield strength of RGLS is 71.5 MPa, much higher than that of the uniform sample (46.5 MPa), despite having a similar relative density of about 46%. The calculated Gibson-Ashby equation and the deformation behaviour simulation by finite element suggest that the dense outer regions with high load-bearing capability could sustain high applied stress, improving the overall strength of RGLS significantly. The cell proliferation study suggests better biological compatibility of the RGLS than the uniform structures. The findings highlight a novel strategy to improve the performance of additively manufactured artificial implants by bio-inspiration.