In this work, electronic and structural properties of single Al or N atom doped and Al-N co-doped graphyne ( GY) toward hydrogen storage were investigated using DFT-D calculations. Results show that N and Al atoms energetically prefer to lie instead of C-sp in the chain and C-sp2 in the hexagonal ring, respectively. Al or N doping changes conducting nature of GY from semiconductor to metallic. Pristine GY and more stable structures of Al doped, N doped and Al-N co-doped GY were examined for H-2 adsorption. Adsorption energies for the first H-2 molecule are about -0.140, -0.224, -0.141 and -0.288 eV/H-2, respectively. They can hold 4, 9, 7 and 16 H-2 molecules with average adsorption energy of similar to-0.089, -0.158, -0.144 and -0.161 eV/H-2, respectively. Also, the calculated corresponding hydrogen storage capacities reach up to 5.26, 10.17, 8.75 and 16.67 wt%, respectively. Although, effect of Al atom is more than N atom, when both of them co-doped in GY, its electronic and structural properties, as well as hydrogen storage capacity improve, extremely and they have a synergistic effect onto hydrogen adsorption. These findings show that N-Al co-doped GY can be used for designing new hydrogen storage materials in the future.