Adsorption of hydrogen on Al(111), Cu(111), Mg(0001), and Ti(0001) surfaces have been investigated by means of first principles calculation. The calculation of surface energy indicates that Mg(0001) is the most stable surface, while Ti(0001) is the most unstable surface among all the four calculated surfaces. The obtained adsorption energy shows that the interaction between Al and H atoms should be energetically unfavorable, and the adsorption of hydrogen on Mg(0001) surface was found to be energetically preferred. Besides, the stability of hydrogen adsorption on studied surfaces increased in the order of Al (111), Ti(0001), Cu(111), Mg(0001). Calculation results also reveal that hydrogen adsorption on fcc and hcp sites are energetically stable compared with top and bridge sites for Ti(0001), Cu(111), and Mg(0001), while hydrogen adsorbing at the top site of Al (111)