The combination of co-precipitation and dehydration is used to prepare hydrated and dehydrated cupric-cobaltous oxalates (Cu1/3Co2/3C2O4·xH2O, x = 1.4; Cu1/3Co2/3C2O4). Then, the hydrothermal treatment of these binary oxalates with freshly prepared graphene oxide (GO) and then dehydration are subsequently adopted to combine the hydrated or dehydrated oxalate with functionalized graphene oxide (FGO), resulting in another two targets of Cu1/3Co2/3C2O4·xH2O/FGO and Cu1/3Co2/3C2O4/FGO composites. These facilitate the comparative studies on the lithium storage capability of cupric oxalate-containing anode materials enhanced by unavoidable crystal water. As a lithium-ion battery anode, Cu1/3Co2/3C2O4·xH2O possesses a reversible capacity of 565.0 mAh g−1 at 1000 mA g−1 over 200 discharge-charge cycles, higher than that of the dehydrated counterpart (246.1 mAh g−1) but lower than those of FGO-based composites (Cu1/3Co2/3C2O4/FGO ∼ 951.2 mAh g−1; Cu1/3Co2/3C2O4·xH2O/FGO ∼ 1134.9 mAh g−1) continuously cycled at the exactly same conditions. At an ultra-high current density of 2000 or 5000 mA g−1, anode Cu1/3Co2/3C2O4·xH2O/FGO delivers a constant discharge capacity of 935.6 mAh g−1 in the 100th cycle or 388.9 mAh g−1 in the 1000th cycle, indicating a jointly positive effect of crystal water and FGO on the high-rate electrochemical performance of cupric-cobaltous oxalate for the first time.