Heteroepitaxy with large lattice mismatch remains a great challenge for high-quality epifilm growth. Although great efforts have been devoted to epifilm growth with an in-plane lattice mismatch, the epitaxy of 2D layered crystals on stepped substrates with a giant out-of-plane lattice mismatch is seldom reported. Here, taking the molecular-beam epitaxy of 2D semiconducting Bi2O2Se on 3D SrTiO3 substrates as an example, a step-climbing epitaxy growth strategy is proposed, in which the n-th (n = 1, 2, 3…) epilayer climbs the step with height difference from out-of-plane lattice mismatch and continues to grow the n+1-th epilayer. Step-climbing epitaxy can spontaneously relax and release the strain from the out-of-plane lattice mismatch, which ensures the high quality of large-area epitaxial films. Wafer-scale uniform 2D Bi2O2Se single-crystal films with controllable thickness can be obtained via step-climbing epitaxy. Most notably, one-unit-cell Bi2O2Se films (1.2 nm thick) exhibit a high Hall mobility of 180 cm2 V−1 s−1 at room temperature, which exceeds that of silicon and other 2D semiconductors with comparable thickness. As an out-of-plane lattice mismatch is generally present in the epitaxy of layered materials, the step-climbing epitaxy strategy expands the existing epitaxial growth theory and provides guidance toward the high-quality synthesis of layered materials.