In this paper, the reflected and transmitted group delay from a one-dimensional photonic crystal heterostructure with graphene at communication band are investigated theoretically. It is shown that the negative reflected group delay of the beam in this structure can be significantly enhanced and can be switched to positive. The large reflected group delay originates from the sharp phase change caused by the excitation of topological edge state at the interface between the two one-dimensional photonic crystals. Besides, the introduction of graphene provides an effective approach for the dynamic control of the group delay. It is clear that the positive and negative group delay can be actively manipulated through the Fermi energy and the relaxation time of the graphene. In addition, we also investigate the transmitted group delay of the structure, which is much less than the reflected one. The enhanced and tunable delay scheme is promising for fabricating optical delay devices like optical buffer, all-optical delays and other applications at optical communication band.