Generally, the global histogram equalization of contrast enhancement methods was used in various application fields because of its simple and effective function. But, as it has a disadvantage that the brightness of an image is changed excessively, in spite of heavy computational complexity, overlapped sub-block histogram equalization method reflecting local histogram properties is used mainly. Also, the global and local histogram equalization methods increase excessively the contrast of simple background occupying wide scope, and they causes the false contour which is unpleasant to the perception operation of an observer. So, in order to improve the local brightness, this paper derived the local histogram equalization (LHE) with the minimal overlapped block size that is optimized for Full High Definition (FHD: 1920×1080) representing the standard image size of large-size LCD (Liquid Crystal Display) TV and can be applied without causing the blocking artifacts, and then it proposed the image contrast enhancement method that combines the modified error diffusion (ED) method in order to reduce the contouring artifacts. This experimental results show that the proposed contrast enhancement method preserves the local image brightness and suppresses the contouring artifacts.