New high-porous fullerene-like molecular forms of carbon (graphyne-like fullerenes) are proposed and their optimized structures, energies, electronic properties, and chemical bonding are investigated by means of ab initio calculations. These cage-like structures are generated using recently predicted new carbon (sp+sp2) allotrope - hexagonal α-graphyne. The graphyne-like analogues of "classical" Buckminster-fullerene C 60 and the smallest fullerene C20 (g-C240 and g-C80, respectively) are studied and compared with conventional graphite-like isomers C240 and C80.