An　efficient　hybrid　system　integrating　a　direct　carbon　fuel　cell　(DCFC)　with　a　vacuum　graphene-anode　thermionic　converter　(VGTC)　is　proposed　for　cogeneration.　The　VGTC　efficiently　recycles　waste　heat　released　from　the　DCFC　and　generate　additional　electricity,　significantly　improving　energy　utilization　efficiency　and　economic　performance.　A　comprehensive　mathematical　model　is　developed　to　quantitatively　assess　the　thermodynamic　performance　of　the　hybrid　system,　taking　into　account　the　overpotential　losses　of　the　DCFC　and　the　irreversible　energy　losses　occurring　within　the　system.　The　results　show　that　at　an　operating　temperature　of　923　K,　the　hybrid　system　can　achieve　a　maximum　power　density　of　466　W/m2,　which　is　approximately　1.34　times　that　of　a　single　DCFC,　indicating　a　significant　improvement　in　output　performance.　Besides,　the　optimal　operating　region　and　parameter　selection　criteria　for　the　hybrid　system　are　determined　using　finite-time　thermodynamic　optimization　theory.　Furthermore,　the　effects　of　essential　parameters　on　the　output　performance　of　the　hybrid　system,　such　as　the　operating　temperature　of　the　DCFC,　the　heat　transfer　coefficient,　the　Fermi　level　of　graphene,　the　work　function　of　the　cathode,　the　thermal　emissivity,　and　the　reflectivity　of　the　back　mirror,　are　investigated.　Finally,　the　comparative　study　shows　that　the　proposed　hybrid　system　outperforms　other　previously　reported　hybrid　systems　regarding　output　electric　power　and　conversion　efficiency　due　to　the　efficient　high-grade　waste　heat　recovery　and　energy　conversion　by　the　VGTC.　©　2024　Elsevier　B.V.