In this paper, we have investigated the superconducting proximity effect in undoped graphene, which is connected to a superconductor, with solving Dirac- Bogoliubov- de Gennes equation (DBdG).We obtain that while the major part of the Andreev bound states appears in propagating modes in the ballistic two- dimensional electron gas (2DEG), graphene system presents evanescent modes in addition to the propagating modes. As a result of the contribution of the evanescent modes, we find the proximity density of states for undoped graphene depends on its distance from the place of superconductor-normal (SN) junction in contrast with the results of 2DEG, showing that the behaviour of undoped graphene is similar to that of the diffusive junctions.