The guided modes are studied in a four-layer left-hand meterial (LHM) slab waveguide structure with a negative refractive material core and three traditional dielectric layer. The graphical method is applied to determine the TE guided modes. The LHM waveguide supports both oscillating guided modes and surface guided modes. The guided modes in the four layer LHM waveguide have some new properties compared to the three-layer waveguide. When the oscillating field exists both in the inner traditional dielectric layer and in the LHM layer,the fundamental mode appears and some high-order modes are absent. And when surface guided modes exist in the LHM layer with the oscillating field in the inner dielectric layer,mode double-degeneracy appears for the high-order modes. The four-layer LHM waveguide is equivalent to the asymmetric three-layer waveguide when the evanescent field exists in the inner dielectric layer. These novel properties are valuable for the fabrication of the optical waveguides in the future.