The emergence of topological order in graphene is in great demand for the realization of quantum spin Hall states. Recently, it is theoretically proposed that the spin textures of surface states in topological insulator can be directly transferred to graphene by means of proximity effect. Here we report the observations of the topological proximity effect in the graphene-topological insulator Bi2Se3 heterojunctions via magnetotransport measurements. The coupling between the p_z orbitals of graphene and the p orbitals of surface states on the Bi2Se3 bottom surface can be enhanced by applying perpendicular negative magnetic field, resulting in a giant negative magnetoresistance at the Dirac point up to about -91%. An obvious resistivity dip in the transfer curve at the Dirac point is also observed in the hybrid devices, which is consistent with the theoretical predictions of the distorted Dirac bands with unique spin textures inherited from Bi2Se3 surface states.