Chemical vapor deposition is widely utilized to synthesize graphene with controlled properties for many applications. And it is one of the most important methods for the preparation of graphene with high quality in large area. Cu substrate is most commonly used for the preparation of graphene in chemical vapor deposition. As is well known, the properties of graphene are greatly affected by the number of layers. However, the syntheses and mechanisms of bi-layer and multi-layer graphene on Cu substrates are still under debate. And how to make a breakthrough in realizing the controllable syntheses of bi-layer and multi-layer graphene on Cu substrates has become a direction for many researchers. In this work, we report bi-layer and multi-layer graphene on Cu substrates prepared by atmospheric pressure chemical vapor deposition. Firstly, the Cu foil is placed on the quartz slides of the tube furnace and heated to 1000℃ with a rate of 15℃/min. After reaching 1000℃, the Cu foilis annealed for 2 h in a gas mixture of hydrogen (20 sccm) and argon (380 sccm). After that, the graphene growth is carried out at 1000℃ under an 80 sccm gas mixture of argon and ethanol. Then, the samples are cooled down to the room temperature with a rate of 100℃/min in a protection gas of hydrogen and argon, and then taken out of the furnace. The graphene is prepared on the Cu foils and finally transferred onto the SiO2/Si substrates. The quality and number of layers of the as-produced graphene are assessed by field emission scanning electron microscopy (SEM), transmission electron microscopy (TEM), Raman spectroscopy, and optical microscopy. By tuning the graphene growth, the monolayer, bi-layer and multi-layer graphene with higer quality and better continuity are obtained. And the growth times of monolayer, bi-layer, and four-layers graphene are respectively 25, 40, and 60 s. And wefind that the graphene layer will be increased in the process of insulation. The growth mechanisms of bi-layer and multi-layer graphene on copper substrates by atmospheric pressure chemical vapor deposition are also discussed. There will be some indiffusible carbon atoms or radicals near the copper foil surface due to the small molecular diffusion mean free path under normal pressure. We suggeste that the bi-layer and multi-layer graphene grown on copper substrates by atmospheric pressure chemical vapor deposition is dominated by van der Waals epitaxial mechanism. This work provides a reference for improving the quality of chemical vapor deposition monolayer, bi-layer and multi-layer graphene.