We study a nonlocal biharmonic MEMS equation with the fringing field. It arises in the Micro-Electro Mechanical System (MEMS) devices. First, we establish the local solution and extend it globally in time. Next, we discuss the dynamical properties of omega limit set. Especially, we show that the omega limit set is included in the set of the stationary solution. Finally, we consider the convergence rate to the stationary solution.