The surface structures of atomic hydrogen adsorbed on Cu(1 1 1) surface have been studied theoretically by using density-functional-theory calculations. The results show that 0.67 ML hydrogen adsorbed on threefold hollow sites forming (3 × 1) superstructure and 0.5 ML hydrogen adsorbed on threefold hollow sites forming (2 × 2)-2H superstructure with central H at trigonal sites induce most significant substrate reconstructions and that fits best the observed (3 × 3) and (2 × 2) LEED patterns, respectively. The potential energies for the hydrogen in these two models are also lower than those in other competing models. Accordingly, these two models are the most preferable structures for 0.5–0.67 ML and 0.3–0.5 ML hydrogen adsorbed on the Cu(1 1 1) surface. In addition, the calculations also suggest that the lateral H–H interaction is not of simple repulsion and how the adsorbed hydrogen is arrayed is important in modifying the adsorption energy.