Display apparatus having different driving frequencies for moving and still image modes and method thereof

A display apparatus includes a display panel including pixels, a gate driver applying a gate signal to a gate line, a data driver applying a data voltage to a data line and a driving controller determining a mode of an input image data to a moving image mode or a static image mode according to whether the input image data is a moving image or a static image, driving the display panel in a moving image driving frequency in the moving image mode and in a static image driving frequency in the static image mode, operating the gate driver in an alternate driving mode such that the gate driver scans a first group of the gate lines in a first duration and a second group of the gate lines in a second duration and inserting a compensation frame to scan all of the gate lines when an image transition is occurred in the static image mode.