Graphene hybrid composite is produced through pyrolysis of a solid carbon source using a specific catalyst. At different catalyst concentrations, different carbon nanostructures like carbon nanotubes or graphene platelets are produced. Graphene hybrid composite produced with an intermediate catalyst concentration shows high conductivity, higher than carbon nanotubes or graphene flakes alone. It has applications as an electrode material for lithium batteries, in super capacitors, and as a conductive material.