The hydraulic-jump phenomenon of a thin fluid layer flowing down an inclined plane under an electrostatic field is explored by using a global bifurcation theory. First, the existence of hydraulic-hump wave has been found from heteroclinic trajectories of an associated ordinary differential equation. Then, the jump behavior has been characterized by introducing an intensity function on the variations of Reynolds number and surfave-wave speed. Finally, we have investigated the nonlinear stability of traveling shock waves triggered from a hydraulic jump by integrating the initial-value problem directly. At a given wave speed there exists a certain value of Reynolds number beyond which a time-dependent buckling of the free surface appears. Like the other wave motions such as periodic and pulse-like solitary waves, the hydraulic-jump waves are also found to become more unstable as the electrostatic field is getting stronger.