The propagating characteristics of a symmetrical three-layer slab waveguide with mu-negative (MNG) media are studied in detail. It is found the MNG waveguide can propagate not only quick waves but also slow waves of TE0 and TE1 modes. The properties of this guided mode are different from those of the left-handed waveguide and the conventional waveguide. In MNG slab waveguide, the region of effective refractive index of the guided mode is wider than those of the other two. In addition, the TE0 fundamental guided mode does not exist at all, while the higher-order TE guided modes and all TM guided modes do exist. However the surface wave of TE0 and TE1 modes can emerge under a certain condition. The propagation constant of higher-order TE mode is greater than that of the TM mode of the same order. Two TE modes of the same order can coexist in the MNG, which is closely related to the structural parameters. The energy fluxes of two TE modes are oppositely directed inside and outside the inner layer, therefore the total energy flux can be negative.