Na-decorated single- and double-sided graphyne and their BN analogs have been proposed to be promising hydrogen storage candidates. The structural stability of metal/graphyne and metal/BN and the metal adsorption sites on the layers were studied in virtue of density-functional theory calculations. Hydrogen storage behaviors on the complexes were investigated. The calculated results demonstrated that each Na atom could attach at most three hydrogen molecules without any dissociation of molecule structures. For Na-decorated double-sided graphyne and EN analog, the hydrogen storage capacities could reach to 5.98 and 5.84 wt%, with the average adsorption energies of -0.25 and -0.17 eV/H-2, respectively. The hydrogen binding mechanisms are unrevealed by analyzing the charge transfer and density of states of the systems. Copyright (C) 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.