The propagation properties,three-layer asymmetric slab wave-guide,is analyzed by using Maxwell's equations when medium 1 and 3 are the left-handed materials and medium 2 is a conventional material.A dispersion relation for TE modes is found.Furthermore,an effective thickness for left-handed slab wave-guide structure is obtained by means of the energy density flux over the period.The dispersion relation,the effective thickness,slab wave-guides are given.The calculated results have been compared with that of righthanded slab wave-guides.We explore more new and unusual characteristics of the guided optical modes in the asymmetrical slab wave-guide structure with left-handed materials.