Regarding crystalline film growth on large lattice-mismatched substrates, there are two primary modes by which thin films grow on a crystal surface or interface. They are Volmer-Weber (VW: island formation) mode and Stranski-Krastanov (SK: layer-plus-island) mode. Since both growth modes end up in the formation of three-dimensional (3D) islands, fabrication of single crystalline films on lattice-mismatched substrates has been challenging. Here, we demonstrate another growth mode, where a buffer layer consisting of 3D islands initially forms and a relaxed two-dimensional (2D) layer subsequently grows on the buffer layer. This 3D-2D mode transition has been realized using impurities. We observed the 3D-2D mode transition for the case of ZnO film growth on 18%-lattice-mismatched sapphire substrates. First, nano-sized 3D islands grow with the help of nitrogen impurities. Then, the islands coalesce to form a 2D layer after cessation of the nitrogen supply, whereupon an increase in the surface energy may provide a driving force for the coalescence. Finally, the films grow in 2D mode, forming atomically flat terraces. We believe that our findings will offer new opportunities for high-quality film growth of a wide variety of materials that have no lattice-matched substrates.