Rational design of novel electrode materials with higher capacity is a key to further improve the energy density of Li-ion batteries (LIBs). Inspired by the high capacity of silicon anode, we here report for the first time a theoretical first-principles investigation into the scientific feasibility of using siligraphene (g-SiC5 and g-SiC2) as a high-capacity anode material for LIBs. The results show that siligraphene working as an LIB anode possesses the advantages of high stability from graphene and high capacity from silicene. While the pristine graphene offers limited Li storage capacity due to the weak Li/graphene interaction, the fundamental Li-Si chemistry ensures a strong Li adsorption in siligraphene and thus allows more Li to be stored. The monolayer siligraphene g-SiC5 and g-SiC2 can be lithiated into Li5SiC5 and Li5Si2C4, respectively, offering a respective theoretical capacity of 1520 mAh/g and 1286 mAh/g. On the other hand, the unique two dimensional honeycomb structure of siligraphene promotes a high electron and Li-ion conductivity to achieve fast cycling rate with negligible volume expansion. The mechanisms on how Si in siligraphene enhances Li/siligraphene interaction are particularly discussed. Overall, the results of this study provide a solid theoretical foundation for rational design of Si/C compounds as novel anode materials for high-performance LIBs.