A graphical method is used to systematically investigate the mode characteristics of an asymmetrical three-layer slab waveguide clad with different single-negative materials. It is demonstrated the waveguide has unusual properties dramatically different from those of conventional waveguide and left-handed material waveguide. The effective refractive index of transverse oscillating guided modes lies in a wider region. In addition, the high-order modes are transverse oscillating guided modes in the core region, only the zero-order one is a surface wave mode. The dispersion curves of high-order TE- and TM- polarized guided modes are nearly the same. The constitutive parameters of single-negative materials have considerable influence on zero-order guided mode. Under certain condition in the waveguide, complete disappearance of zero-order modes, only surface wave propagation, superslow wave, and zero-order dual modes of backward waves will occur.