The adsorption of a single polymer chain onto a solid surface is investigated by molecular dynamics simulations. The chain is composed of mass points interacting via a truncated Lennard-Jones potential, i.e., the excluded volume interaction is taken into account, and grafted to the surface with one end. The average adsorption degree is calculated for various chain lengths (N = 16, 32, 64, 128) and adsorption energies. In addition, the scaling behavior of the adsorption degree and the radius of gyration is investigated. The adsorption degree and the average length of loops and tails are obtained for chains of various stiffnesses. In this context, we find that stiffer chains adsorb more easily. Moreover, the distribution of the mass points perpendicular to the surface as well as the orientation of the bonds with respect to the surface is discussed for various adsorption energies and stiffnesses.