An asymmetric three-layer slab waveguide with a core of the left-handed material and sandwiched by two conventional materials is investigated. Considering the dispersive and an isotropic properties of the left-handed material, the dispersion equation and power fluxes for TE oscillating guided modes are obtained and mode dispersion curves are plotted,respectively, through Maxuell′s equations. Eight TE oscillating guided modes are found, including the fundamental mode. With the increase of mode number, mode dispersion curves move to right and the power flux curves move to right bottom. However, with the increase of waveguide thickness, mode dispersion curves move to left and mode power flux curves move up. Besides, all modes have abnormal dispersion properties and employ negative group velocities which reveals the special properties of the left-handed materials.