When a parallel-plate electrostatic actuator (ESA) is driven by a voltage source, pull-in instability limits the range of displacement to one-third of the gap between plates. In this paper, a nonlinear active disturbance rejection controller (NADRC) is originally developed on the ESA. Our control objectives are stabilizing and increasing the displacement of an ESA to 99.99% of its full gap. Most of the reported controllers in literature are based on linearized models of the ESAs and depend on detailed model information of them. However, the ESA is inherently nonlinear and has model uncertainties due to the imperfections of microfabrication and packaging. The NADRC consists of a nonlinear extended state observer (NESO) and a feedback controller. The NESO is used to estimate system states and unknown nonlinear dynamics for the ESA. Therefore, it does not require accurate model. We simulate the NADRC on a nonlinear ESA in the presences of external disturbance, system uncertainties, and noise. The simulation results verify the effectiveness of the controller by successfully extending the travel range of ESA beyond pull-in point. They also demonstrate that the controller is robust against both disturbance and parameter variations, and has low sensitivity to measurement noise. Furthermore, the stability for the control system with NADRC is theoretically proved.