A theory is presented for exciton formation in a graphene sheet using the center-of-mass approximation. The energy levels and wavefunctions of exciton are calculated analytically which show that the exciton can form if the band gap of graphene is not zero. We show that the energy gap of graphene plays the role of the mass which if not zero, leads to formation of the excitons. It is shown that the main quantum number of the excitonground state changes with the graphenedielectric constant. Also, all of the states are found to be four-fold degenerate. The binding energy of exciton can reach as high as 1/4 of the energy gap of graphene which is notable among the conventional quasi-2D systems. This result can play an important rule in the photonics of graphene.