Motivated by the inability of the existing local voltage control schemes to stabilize the voltages to within the acceptable ranges, we propose a new local voltage control algorithm where each bus adjusts incrementally its reactive power in response to its voltage deviation from the nominal value. We show that the dynamical system with the proposed incremental control can be seen as a distributed algorithm for solving a well-defined optimization problem that minimizes the cost of voltage deviation, and give a sufficient condition under which the dynamical system converges. This optimization-based characterization of equilibrium and dynamical properties of the incremental local voltage control suggests a straightforward way to stabilize the distribution system to within the desired acceptable voltage ranges by simply specifying the control function's deadband as the acceptable voltage range. Numerical examples with a real world distribution circuit are provided to complement the theoretical analysis.