An apparatus for encoding an image data includes a sub-pixel rendering unit and a first differential pulse code modulation (DPCM) processing unit. The sub-pixel rendering unit converts first image data of an RGB type to second image data of an RG-BG type. The DPCM processing unit generates first differential data including primary differential values corresponding to respective sub-pixels. To perform this operation, the DPCM processing unit calculates a gray value difference from a neighboring sub-pixel for each of the sub-pixels based on the second image data.