It has been recently demonstrated that negative-index dispersion and mode degeneracy can be achieved by manipulating a spoof-insulator-spoof(SIS) waveguide. In this paper, we propose a new SIS waveguide, which is composed of two spoof surface plasmon polaritons(SSPPs) waveguides drilled with periodic rhomboidal grooves. Both the symmetric and asymmetric cases are investigated. Our simulation results show that the asymmetric SIS waveguides are more significant.By tailoring the tilt of the rhomboidal grooves, the negative-index dispersion can be achieved and the microwave band gap(MBG) can be effectively modulated. At a critical tilt, there appears an accidental mode degeneracy at the edge of the first Brillouin zone. The excitation and propagation of the two coupled modes sustained by the asymmetric SIS waveguides are also demonstrated. It has been recently demonstrated that negative-index dispersion and mode degeneracy can be achieved by manipulating a spoof-insulator-spoof (SIS) waveguide. In this paper, we propose a new SIS waveguide, which is composed of two spoof surface plasmon polaritons Both the symmetric and asymmetric cases are investigated. Our simulation results show that the asymmetric SIS waveguides are more significant. By tailoring the tilt of the rhomboidal grooves, the negative-index dispersion can be achieved and the The excitation and propagation of the two coupled modes sustained by the asymmetric SIS waveguides are also demonstrated.