A data driver includes two data processing circuits for respectively providing positive and negative pixel voltages according to first and second pixel data, and a multiplexer circuit including multiplexer units. Each multiplexer unit has first and second input terminals respectively receiving the positive and negative pixel voltages, and an output terminal coupled to a data line. A first switching device has first and second switches serially coupled between the first input and output terminals. A node between the first and second switches is selectively grounded via a third switch. A second switching device has fourth and fifth switches serially coupled between the second input and output terminals. A node between the fourth and fifth switches is selectively grounded via a sixth switch. When the first and second switches turn on, the sixth switch turns on. When the fourth and fifth switches turn on, the third switch turns on.