Data driver and driving method with control of bias current based on pixel image data

A data driver includes buffers respectively outputting data voltages corresponding to pixel image data, bias units corresponding to the buffers in a one-to-one correspondence and driving the buffers, respectively, and a global setting part applying control level values to the bias units. Each of the bias units includes a bias signal generating unit that selects one control level value among the control level values based on a corresponding pixel image data among the pixel image data and generates a bias signal having a control level corresponding to the selected control level value and a current generating unit that generates a corresponding bias current in response to the bias signal and applies the corresponding bias current to a corresponding buffer among the buffers.