We investigate the adsorption of Na atoms on pristine graphene and four types of defect graphenes using the first-principles calculations. The adsorption energies, electronic structures, Na storage capacities and the average potentials of Na atoms on different graphenes are calculated. The adsorption energies of Na atoms on B-doped, vacancy and B-doped vacancy graphenes are -1.93 eV, -2.46 eV, and -2.08 eV, respectively, which are much lower than that of Na on the pristine graphene (-0.71 eV) and Na on N-doped graphene (-0.27 eV). The orbital hybridizations in the B-doped, vacancy and B-doped vacancy graphenes can be observed from the partial density of states, while there is no obvious orbital hybridization in the N-doped graphene as well as the pristine graphene. The B-doped vacancy graphene has the best Na storage capacity, while B-doped and vacancy graphenes also possess better Na storage capacities than those of the pristine graphene and N-doped graphene. This work demonstrates that the graphene introducing both B dopant and vacancy is expected to be a potential material for storing Na. (C) 2016 Elsevier B.V. All rights reserved.