For electromagnetic plane wave propagating in nonlinear left-handed material,the properties of nonlinear TE surface waves localized at the interface of a left-handed material(an interface separating a left-handed material and a right-handed material or an interface separating two left-handed materials) are investigated in detail. The results of frequency characteristics prove there exist both passband(s) and stopband(s),which have the wave power-dependent properties and can be controlled by varying the power in the waveguide. The frequency dispersion and variation of group velocity with frequency are also calculated. Base on the analysis,the interface between a nonlinear left-handed material and a right-handed material can support both forward TE surface waves and backward TE surface waves under certain conditions. Whereas,the relative properties are quite different when the surface waves localize at the interface between two left-handed materials,there only can exist backward waves according to certain conditions.