Support structure plays an important role on sustaining overhang areas, resisting shape deformation and reducing thermal stress in many additive manufacturing (AM) processes. However, design of support structures in the preparation stage and removing of those structures in the post-processing stage are still time-consuming and costly. To reduce support structure volume, post-processing time and improve the printing quality, this paper proposes a novel enhanced bio-inspired generative design method, integrating parametric L-system rules and lattice structure configuration, to generate lightweight, easy-to-remove and heat-diffusion-friendly biomimetic support structures. A complex dental component with freeform geometries and discontinuous support areas is selected as a case study to compare with existing popular support design methods. The comparison results show the proposed method exhibits a good support performance for complex dental overhang areas. Hence it has potential to be adopted for other AM processes where support structures are required.