In this paper, we study the slow propagation characteristics of surface electromagnetic waves according to theoretical analysis in the MNG (μ-negative)-DPS (double-positive)-MNG waveguide, which is composed of two-dimensional (2D) metamaterials. The dispersion curves of this waveguide vary with circuit parameter (unit capacitors) of MNG metamaterial. At the cutoff frequency of the dispersion curve the group velocity of electromagnetic wave is equal to zero in theory. So we can obtain slow propagation of the surface waves at different cutoff frequencies just by changing the unit capacitor of the MNG metamaterial. Theoretical analysis also shows that the step changes in slow waves are obtained at some fixed frequencies through changing the unit circuit parameters. The experimental results are in good agreement with simulation results.