We have studied the adsorption and desorption of atomic hydrogen on the surfaces of Ag thin films. Atomically flat Ag films were grown on Au(111), exposed to a flux of thermally generated hydrogen atoms at a low sample temperature, and annealed for the desoprtion of hydrogen atoms. During annealing, the evolutions of the surfaces of the thin films were characterized on monitoring their surface states with angle-resolved photoemission spectroscopy. Our experimental results showed that, with the exposure of hydrogen atoms, the surfaces states of thin Ag films deteriorated severely, and the surface states recovered only partially during annealing. In addition, we also investigated the relationship between the deterioration of the surface states and the thickness of the thin films.