First-principles calculations are performed to identify the pristine and Si doped 3D metallic T6 carbon structure (having both sp2 and sp3 type hybridization) as a new carbon based anode material. The π electron of C2 atoms (sp2 bonded) forms an out of plane network that helps to capture the Li atom. The highest Li storage capacity of Si doped T6 structure with conformation Li1.7Si1C5 produces theoretical specific capacity of 632 mAh/g which substantially exceeding than graphite. Also, open-circuit voltage (OCV) with respect to Li metal shows large negative when compared to the pristine T6 structure. This indicates modifications in terms of chemical properties are required in anode materials for practical application. Among various doped (Si, Ge, Sn, B, N) configuration, Si doped T6 structure provides a stable positive OCV for high Li concentrations. Likewise, volume expansion study also shows Si doped T6 structure is more stable with less pulverization and substantial capacity losses in comparison with graphite and silicon as an anode materials. Overall, mixed hybridized (sp2 + sp3) Si doped T6 structure can become a superior anode material than present sp2 hybridized graphite and sp3 hybridized Si structure for modern Lithium ion batteries.