The frequency range that surface plasmon polariton (SPP) mode exists is mainly limited by the metal material. With high permittivity dielectrics above metal surface, the SPP mode at high frequency has extremely large loss or can be cutoff, which limits the potential applications of SPP in the field of optical interconnection, active SPP devices and so on. To extend the frequency range of SPP mode, the surface mode guided by metal/dielectric multilayers meta-material has been studied based on the theory of electromagnetic field. It is demonstrated that surface mode not only could be supported by the meta-material but also extends the frequency to where conventional metal SPP cannot exist. Meanwhile, the characteristics of this surface mode, such as dispersion relation, frequency range, propagation loss and skin depth in meta-material and dielectrics, are also studied. It is indicated that, by varying the structure parameters, the meta-material guided SPP mode presents its advantages and flexibility over traditional metal one.