The operation analysis of a new interface circuit for electrostatic vibration energy harvesting with adjustable bias voltage is carried out in this paper. Two configurations determined by the open or closed states of an electronic switch are examined. The increase of the voltage across a biasing capacitor, occurring when the switch is open, is proved theoretically and experimentally. With the decrease of this biasing voltage which occurs naturally when the switch is closed due to imperfections of the circuit, the bias voltage can be maintained close to a target value by appropriate ON and OFF control of the switch. As the energy converted by the variable capacitor on each cycle depends on the bias voltage, this energy can be therefore accurately controlled. This feature opens up promising perspectives for optimization the power harvested by electrostatic devices. Simulation results with and without electromechanical coupling effect are presented. In experimental tests, a simple switch control enabling to stabilize the bias voltage is described.