TE guided modes at microwave frequencies in metal-left-handed material-ferrite waveguide structures are studied numerically. The effect of ferrite layer parameters on the dispersion properties of the waveguide structure is investigated in details. It is found that the modal index of the guided mode is negative as if the overall structure was left-handed material. A considerable effect of the gyromagnetic ferrite layer on the dispersion properties of the structure is observed. The power propagating in each layer is also evaluated.