Abstract.  An asymmetric negative-zero-positive index metamaterial (NZPIM) waveguide with two different Dirac points (DPs) operating in the terahertz (THz) regime is proposed. Its propagating characteristics are investigated by using the graphical method. Due to the linear dispersion near the DPs, the asymmetric NZPIM waveguide exhibits unique properties of guided modes, which are different from that in conventional waveguide but similar to that of electron waves in graphene waveguides. It is shown that the guided mode properties can be tuned by adjusting the incident angular frequency. In addition, the properties of surface-guided modes are also discussed. Our work may have potential applications in THz functional devices as well as reference value in investigating the guided modes of electrons in graphene waveguides.