For TE electromagnetic waves propagating at the interface of a conventional nonlinear material and a negative refraction material, the properties are investigated in detail. The results prove that there exist pass bands, which have the material-dependent properties. Base on the analysis, the interface supports both forward and backward TE surface waves which can change each other under certain conditions. The electric field amplitude in the two materials is also studied. It’s found that the two amplitudes can change from one material to the other with the difference of energy flux. Both of the two amplitudes are near the interface, one is almost at the interface.