This paper presents a new interface circuit for electrostatic vibration energy harvesting with adjustable bias voltage. An electronic switch is used to modify the circuit configuration so that the harvested energy increases the voltage across a biasing capacitor. Decrease of this biasing capacitor voltage occurs naturally due to the circuit imperfections. Such a control of the bias voltage enables to adjust the amount of energy converted by the variable capacitor on each cycle. This feature can be used to optimize the mechanical damping induced by the energy conversion process in order to maximize the harvested power. Another feature of this interface circuit is that it is capable to get high bias voltage whatever the battery voltage with low energy loss.