Abstract The propagation characteristics of TE0 modes is studied in an asymmetric leaky waveguide of Kerr-type dielectric film under certain boundary condition. Our result shows that steady guided wave cannor exist if the film thickness is greater than a critical value, and two TE0 modes with different wave numbers may exist if the film thickness is less than that critical value. The propagating powers and the positions of the field amplitude peaks of these two modes in the film vary quite differently when the film thickness or the wave frequency changes. The dispersion relations of these two modes are also different. In the limit of symmetric structure, the dispersion of the weaker TE0 mode is zero.