1. An image encoding apparatus for encoding data of an inputted image and outputting encoded image data, comprising: an image-size-condition storage which stores an image-size condition including image size and target sharpness; an image-size reduction unit which produces a reduced image of said inputted image having said image size included in said image-size condition stored in the image-size-condition storage; a sharpness calculation unit which calculates sharpness of said reduced image; and an image-size control unit which reduces said image size included in said image-size condition stored in the image-size-condition storage and makes said image-size reduction unit further reduce said inputted image to the reduced image size, when the sharpness of said reduced image calculated by the sharpness calculation unit is higher than said target sharpness.