For linear TE electromagnetic plane waves propagating in a conventional waveguide bounded by symmetrical left-handed media,the guide modes are discussed in detail by looking for the intersections of curves,which are determined by the boundary conditions. The results prove that both fast waves and slow waves can propagate in this peculiar waveguide system,and the relevant properties of the waves are quite different from which in conventional waveguide and left-handed waveguide. The frequency dispersion and group velocity are also considered. Base on the analysis,it can be concluded that this waveguide can support both forward linear TE waves and backward linear TE waves under certain conditions.