The prevalent concept is that a topological insulator is made of thick layers of atoms so that its surfaces, where electrical conduction occurs, can be distinguished from the insulating bulk of the interior. One important reason is that the thin film topological insulator may cause the opening of energy band gaps by quantum tunneling between the two surfaces. Inspired by an experiment on antimony thin films, we use density functional calculations to investigate the electronic structure of the four-bilayer Sb film and find that adsorptions of nonmagnetic impurity atoms of hydrogen and 3d transition-metal atoms on the film all close the energy gap of the free-standing film and facilitate the formation of Dirac cones that preserve time-reversal symmetry. However, magnetic atoms of the 3d transition metals do just the opposite. The results suggest the counterintuitive concept of achieving topological conduction by doping nonmagnetic impurity atoms on thin films of topological insulators.