In this paper, we study the following nonlinear equation with mean curvature-like operator$$\frac{\partial q(x,t)}{\partial t}+\frac{\partial}{\partial x}(\frac{\frac{\partial q(x,t)}{\partial x}}{\sqrt{1+(\frac{\partial q(x,t)}{\partial x})^{2}}})-g( q(x,t))=0.$$ By using the theorem of the monotone dynamical system, the existence conditions of traveling wavefronts is established.
