The propagation properties of TE mode in three layer slab waveguides with left-hand materials as substrate and single-negative materials as cover layer were investigated, providing theoretical support for the design of waveguide device. The dependence of normalized effective waveguide thickness on normalized frequency for the modes of three layer slabs was worked out. The propagation properties of TE mode in three slab waveguides were analyzed. The results show that the change rate of the normalized effective refractive index with normalized effective frequency is decreased with increasing the ratio of permeability of guided wave layer to substrate or superstratum. As the asymmetric value approaches to zero, varies with monotonically. While the asymmetric value is big enough, there is two-value phenomenon for TE, TE, TE, TE and TE modes near cutoff frequency. When the asymmetric value increases, the curve-shifts from left to right. will be negative for TE mode.