A symmetric five-layer slab waveguide with a core of left-handed material and surrounded by four normal dielectrics is investigated.Under the consideration of material dispersion,the dispersion equations for the TE oscillating guided modes are obtained and mode dispersion curves are plotted.It is found that zero-order TE oscillating guided mode is exist.With the increase of mode number,mode dispersion curves move to left,and their cutoff frequencies decrease.Besides,some modes have three dispersion properties: normal dispersion,abnormal dispersion and mode double-degeneracy.