Using the first-principles density functional theory, the hydrogen storage properties of monolayer and bilayer α-graphyne systems decorated by alkali metal are investigated. The results of band structure and density of state analysis indicate that alkali metal decoration enhances the chemical activity of the adsorption substrate, leading to increased H2 adsorption capacities for Li, Na and K decorated monolayer systems (15.0 wt.%, 14.5 wt.%, 10.7 wt.%, respectively). The combined action of interlayer force and decorated metal atoms results in higher H2 adsorption capacities for Li, Na and K decorated bilayer systems (17.7 wt.%, 16.9 wt.%, 13.0 wt.%, respectively), which means the bilayer graphyne structures enhance the storage capacities for decorated structures. Additionally, the Na decorated rhombus bilayer system demonstrates the highest adsorption density of H2 molecules between α-graphyne layers. Overall, alkali metal decorated monolayer and bilayer systems exhibit promising H2 adsorption potentials.