The fabrication of organic semiconductor thin films is extremely important in organic electronic devices. This tutorial review—which should particularly appeal to chemists and physicists interested in organic thin-film growth, organic electronic devices and organic semiconductor materials—summarizes the method of weak epitaxy growth (WEG) and its application in the fabrication of high quality organic semiconductor thin films. WEG achieves the thin-film fabrication of disk-like organic semiconductor molecules with highly structural order, molecular level smoothness and large size domains on amorphous substrate. The organic field-effect transistor devices based on these thin films exhibit a high charge mobility that is comparable with their corresponding single-crystal devices. Moreover, it provides a way to produce organic superlattices.