The adsorption of H2 on Ce doped single-walled carbon nanotubes (SWCNT) and graphene are investigated by using density functional theory. For both systems, it is found that Ce preferentially occupies the hollow site on the outside. The results indicate that Ce/SWCNT system is a good candidate for hydrogen storage where six H2 per Ce can be adsorbed and 5.14 wt% H2 can be stored in the Ce3/SWCNT system. Among metal-doped SWCNTs, Ce exhibits the most favorable hydrogen adsorption characteristics in terms of the adsorption energy and the uptake capacity. The hybridization of the Ce-4f and Ce-5d orbitals with the H orbital contributes to the H2 binding where Ce-4f electrons participate in the hybridization due to the instability of the 4f state. The interaction between H2 and Ce/SWCNT is balanced by the electronic hybridization and electrostatic interactions. Curvature of SWCNT changes the size of the binding energy of Ce and C and the adsorption energy of H2 on Ce.