The interaction of molecular hydrogen with carbon nanostructures is investigated within the DFT/CC correction scheme. The DFT/CC results are compared with the benchmark calculations at the CCSD(T) level of theory for benzene and naphthalene, and at the MP2 level for the more extended systems. The DFT/CC method offers a reliable alternative to the highly correlated ab initio calculations at a cost comparable to the standard DFT method. The results for H(2) adsorbed on graphene as well as single-wall carbon nanotubes (SWCNT) are presented. The DFT/CC binding energy on graphene of 5.4 kJ mol(-1) is in good agreement with experiment (5.00+/-0.05 kJ mol(-1)). For (10,10)-SWCNT, the H(2) molecule is mostly stabilized inside the tube with an estimated binding energy of 7.2 kJ mol(-1).