The TE oscillating guided modes and their propagation properties in a taper slab waveguide with anisotropic metamaterials are investigated. From Maxwell equations, based on continuous boundary conditions for tangential electromagnetic fields, we obtain a dispersive equation and a power flow equation of TE oscillating guided modes with a variable separation method. Based on the above equations, using a curve fitting technique, we plot some corresponding curves. It is found that the electric field intensity considers the influence of x and z directions, and the power flow changes periodically with the increase of the waveguide length; as the slope of the taper slab waveguide k=0.1, the waveguide length of the guided mode transmission is less than 2.5 mm; as lower frequencies (f=5.0 GHz) and k=0.01,for different mode orders, the variation of waveguide thickness has little effect on power flow transmission. The properties will help us to minimize the waveguide and decrease the accuracy requirement of the waveguide processing in the future.