In this paper, the reflected group delay from a multilayer structure where bulk Dirac semimetals (BDS) is coated on one-dimensional photonic crystal (1D PC) separated by a spacer layer is investigated theoretically. It is shown that the group delay of reflected beam in this structure can be significant enhanced negatively and can be switched from negative to positive. The enhanced group delay originates from the steep phase change caused by the excitation of optical Tamm state (OTS) at the interface between the BDS and spacer layer. Moreover, the positive and negative group delay can be actively tuned through the Fermi energy and the relaxation time of the BDS. We believe that this enhanced and tunable delay scheme has important research significance for fabrication of optical delay devices.