Non-covalent adsorption of proteins onto carbon nanotubes is important to understand the environmental and biological activity of carbon nanotubes as well as their potential applications in nanostructure fabrication. In this study, the adsorption dynamics and features of a model protein (the A sub-domain of human serum albumin) onto the surfaces of carbon nanotubes with different diameters were investigated out by molecular dynamics simulation. The adsorption behaviors were observed by both trajectory and quantitative analyses. During the adsorption process, the secondary structures of alpha-helices in the model protein were slightly affected. However, the random coils connecting these alpha-helices were strongly affected and this made the tertiary structure of protein change. The conformation and orientation selection of the protein were induced by the properties and the texture of surfaces indicated by the interaction curve. In addition, the stepwise adsorption dynamics of these processes are found. The mechanism of induced stepwise conformational change of protein on carbon nanotube surfaces would be helpful to better understand the protein-surface interaction at the molecular level.