Abstract: A novel waveguide structure is presented which is filled with materials combined with epsilon-negative and mu-negative. There are many especial electromagnetic characters in this waveguide. The propagation constant is discussed based on electromagnetic fields in waveguide by it＇s boundary condition. The relation among propagation constant, frequence and one of the medium＇s thickness is analyzed under different permittivities, permeabilities and modes. Some different conclusions from conventional rectangular waveguide are presented.