Although graphene based drug delivery has gained significant recent interest, the synthesis of colloidal graphene based nanocarriers with high drug loading capacities and with targeting ligands at the outer surface is a challenging issue. We have synthesized carbohydrate coated and folate functionalized colloidal graphene which can be used as a nanocarrier for a wide variety of hydrophobic and hydrophilic drugs. The synthesized colloidal graphene is loaded with paclitaxol, camptothecin, doxorubicin, curcumin and used for their targeted delivery to cancer cells. We demonstrate that this drug loaded functional graphene nanocarrier can successfully deliver drugs into target cells and offers an enhanced therapeutic performance. The reported approach can be extended to the cellular delivery of other hydrophobic and hydrophilic drugs and the simultaneous delivery of multiple drugs.