This paper describes the propagation models of the transverse electrical wave and current distribution in the superconductor cylindrical waveguide based on superconductor electromagnetic theory and the Meissner model. In the superconductor waveguide

the boundary conditions of conventional metals waveguide are not valid

which must be corrected by Meissner model.Many different electromagnetic properties are found in superconductor cylindrical waveguide because of these new boundary conditions.