Li and Na attachment to free tetracyanoethylene (TCNE) molecules and TCNE adsorbed on doped graphene is studied using density functional theory. While TCNE is adsorbed only weakly on ideal graphene, we identified a configuration in which TCNE is strongly chemisorbed on Al-doped graphene via molecule's C atom and a surface oxygen atom. Up to four (five) Li and Na atoms can be stored on both free (adsorbed) TCNE with binding energies stronger than cohesive energies of the Li and Na metals. When storing up to three atoms per molecule, it should be possible to avoid reduction of common battery electrolytes. TCNE immobilized on a conducting graphene-based substrate could therefore become an efficient anode material for organic Li and Na ion batteries. Importantly, there is no significant difference either in specific capacity (per unit mass of material excluding Li/Na) nor in voltage between Li and Na storage, which makes this kind of approach very promising for post-Li storage in general. (C) 2015 Elsevier B.V. All rights reserved.