We investigated theoretically the existence of surface polaritons (SPs) at the interface of a one-dimensional photonic crystal containing graphene monolayers. It is shown that the structure has a new type of the photonic band gap in the THz region which is strictly omnidirectional for the TM-polarization and can support the SPs for both TM-polarization and TE-polarization. The results show that the characteristics of the SPs depends on the optical properties of the graphene sheets which can be controlled by a gate voltage. We plotted the electromagnetic field profiles of the SPs at the frequency range of the graphene induced band gap and a conventional Bragg gap of the structure. It is found that the SPs at the graphene induced band gap are more localized than the SPs at the Bragg gaps.