The propagation properties in a symmetrical three slabs air waveguide with left-handed materials as substrate and cover layers were studied.The fast and slow waves can both propagate in the waveguide system.There is no base mode for fast wave.The slow wave mode can exist in zero or one order TE or TM mode only.TE and TM mode were degenarated when the permittivity equal to permeability of the left-handed material.And the degenarate was disappeared.Two propagation modes with the same mode number can coexiste in the waveguide.