Westudy a damped hyperbolic MEMS equation with the fringing field. It arises in the Micro-Electro Mechanical System(MEMS) devices. We give some criteria for global existence and quenching of the solution. First we establish a time-local solution by a contraction mapping theorem. This procedure is standard. Next we show that there exists a global solution for the small parameter and initial value. Finally, we deal with the quenching result for the large parameter.