Abstract: By using the first-principles method based on the density functional theory, the formation of a hole on graphene and their electronic structures properties are studied. We have calculated all the structures of holes where number N of carbon atoms (N=1 to 19) are removed from graphene. The results suggest that, as the holes get bigger (N=1, 2, …, 19.), the electronic structures of the system show rich characteristics: metallic, semimetal and semiconductor properties. The calculations show that all the metallic hole systems have dangling bonds at the edge of the holes, and they are weak magnetic if the system is metallic. For the systems with no dangling bond at the edge of the hole, the system can still show semi-metallic, metallic and semiconducting properties. It is particularly interesting that flat bands appear in the band structures of some systems, and we have made a relatively detailed analysis of the electronic structures of the flat bands. In addition, first-principles molecular dynamics simulations show that the hole formed by the removal of 19 carbon atoms is thermodynamically stable.