The nanosized graphene structures have attracted extensive attention in many fields in recent years because of their unique and tunable electronic structures depending on the size,shape,edge,etc.Here we studied electronic structures of some nanosized grapheme quantum dot systems with regular shape based on first-principle calculations.In virtue of the central insertion scheme developed by our group previously,electronic structures of large systems involving thousands of atoms can be solved effectively.Graphene nanodots with rectangular,triangular,rhombic,and hexagonal shape and with armchair and zigzag edge were considered respectively.Energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital,density of states,optical absorption spectrum and polarizabilities of these systems as the function of system size were calculated.Changes of these electronic properties with the increasing size were discussed.These results would be helpful to the practical application of nanosized graphene quantum dots as the basic building blocks in future molecular electronics and other fields.