A common-voltage compensation driving apparatus and method and a crosstalk-compensation driving apparatus of an AMLCD detect current flowing through a common electrode for an optional period to compensate for a common electrode voltage by using the current value as a reference and eliminate crosstalk resulting from the variation of a video data value. The common-voltage compensation driving apparatus includes a current detector for detecting the current flowing through a common electrode for an optional period, a proportional voltage generator for integrating the current detected by the current detector to generate a proportional voltage corresponding to the integrated current, a common voltage generator for compensating the proportional voltage of the proportional voltage generator to a common electrode voltage during a compensating period shorter than one horizontal scanning period, and a controller for controlling driving times of the current detector, proportional voltage generator and common voltage generator. The method therefor is performed by a current detecting step, a proportional voltage generating step, and a common voltage generating step. The crosstalk compensation driving apparatus has the current detector, the proportional voltage generator, a data signal voltage compensator for compensating the proportional voltage of the proportional voltage generator to a data signal voltage output during a compensating period shorter than one horizontal scanning period, and the controller.