Method for manufacturing semiconductor device

A larger substrate can be used, and a transistor having a desirably high field-effect mobility can be manufactured through formation of an oxide semiconductor layer having a high degree of crystallinity, whereby a large-sized display device, a high-performance semiconductor device, or the like can be put into practical use. A first multi-component oxide semiconductor layer is formed over a substrate and a single-component oxide semiconductor layer is formed thereover; then, crystal growth is carried out from a surface to an inside by performing heat treatment at 500° C. to 1000° C. inclusive, preferably 550° C. to 750° C. inclusive so that a first multi-component oxide semiconductor layer including single crystal regions and a single-component oxide semiconductor layer including single crystal regions are formed; and a second multi-component oxide semiconductor layer including single crystal regions is stacked over the single-component oxide semiconductor layer including single crystal regions.