1. An image processing apparatus which processes an image to be displayed on a display, the image processing apparatus comprising: an image receiving unit which receives an image; and an image processing unit which determines a gain value and a threshold value of sharpness of the image according to an original luminance of the image and adjusts the sharpness of the image by adjusting the gain value so that the luminance of the image is within the threshold value, wherein the image processing unit comprises: a gain determination unit which determines the gain value to adjust sharpness of the image based on the original luminance of the image; and a gain adjustment unit which adjusts the gain value determined by the gain determination unit based on the threshold value and adds the adjusted gain value to the original luminance of the image so that the sharpness of the image may be improved, so that the luminance of the image to which the adjusted gain value is added may be within the preset range of luminance measured according to the original luminance of the image based on the threshold value.