In this study, transition metals (TM) such as palladium (Pd) have been introduced on co-doped graphene and defect graphene sheets with nitrogen and boron ad-atoms to investigate the potentials of new adsorbents for hydrogen storage. The first principle studies using density functional theory (DFT) and DFT-D3 correction dispersion were undertaken to calculate the adsorption energy of hydrogen molecule on the graphene sheet. The results showed that applying Pd transition metal could enhance adsorption energy of hydrogen molecules towards pristine sheet. The main problem in applying transition metal on graphene sheets was concerned with clustering. However, the current defects in graphene sheets prevent clustering event. Our simulation results suggested that these defects reduced hydrogen adsorption and substitute dopants such as nitrogen and boron together on graphene sheets could improve the adsorption energy. Thus, two various forms of Pd decorated N B co-doped as hexagonal and double carbon vacancy (DCV) were introduced as new structures for hydrogen storage. A physical adsorption, which is appropriate for reversible hydrogen storage, was implemented for both novel adsorbents. In the two various forms of N B co-doped structures, DCV had the optimum adsorption behavior as adsorption energy level and density of state (DOS) phenomena. Moreover, the results of adsorption energy using DFT method were consistent with that of DFT-D3 correction dispersion and higher amounts of adsorption energy in DFT-D3 method were obtained. Finally, results introduced Pd decorated N B co-doped graphene sheets as a novel material for hydrogen storage. (C) 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.