An image encoding apparatus comprising: a intra-prediction image generating unit for performing intra-frame prediction for a present frame for which a prediction image is to be generated, and for generating an intra-prediction image corresponding to the prediction image from a portion of an image of the frame; characterized by a prediction image generating unit including: a difference calculation unit for calculating a difference image between the intra-prediction image and a motion compensation image corresponding to the intra-prediction image; a low-pass filter unit for applying a low-pass filter to the difference image, thereby arriving at an image obtained by applying the low-pass filter by using the low-pass filter unit, a first gain adjustment unit for adjusting a gain of the image obtained by applying the low-pass filter by multiplying the image obtained by applying the low-pass filter with a first constant factor, thereby arriving at a first gain-adjusted image; high-pass filter unit for applying a high-pass filter to the image obtained by applying the low-pass filter by using the low-pass filter unit, thereby arriving at a filtered image, a second gain adjustment unit for adjusting a gain of the filtered image obtained by applying the high-pass filter by multiplying the filtered image obtained by applying the high-pass filter with a second constant factor, thereby arriving at a second gain-adjusted image; a first adding unit for adding the first and second gain-adjusted images, thereby arriving at an image obtained by addition; and a second adding unit for adding the image obtained by addition to the intra-prediction image generated by the intra-prediction image generating unit, thereby generating the prediction image. a intra-prediction image generating unit for performing intra-frame prediction for a present frame for which a prediction image is to be generated, and for generating an intra-prediction image corresponding to the prediction image from a portion of an image of the frame; characterized by a prediction image generating unit including: a difference calculation unit for calculating a difference image between the intra-prediction image and a motion compensation image corresponding to the intra-prediction image; a low-pass filter unit for applying a low-pass filter to the difference image, thereby arriving at an image obtained by applying the low-pass filter by using the low-pass filter unit, a first gain adjustment unit for adjusting a gain of the image obtained by applying the low-pass filter by multiplying the image obtained by applying the low-pass filter with a first constant factor, thereby arriving at a first gain-adjusted image; high-pass filter unit for applying a high-pass filter to the image obtained by applying the low-pass filter by using the low-pass filter unit, thereby arriving at a filtered image, a second gain adjustment unit for adjusting a gain of the filtered image obtained by applying the high-pass filter by multiplying the filtered image obtained by applying the high-pass filter with a second constant factor, thereby arriving at a second gain-adjusted image; a first adding unit for adding the first and second gain-adjusted images, thereby arriving at an image obtained by addition; and a second adding unit for adding the image obtained by addition to the intra-prediction image generated by the intra-prediction image generating unit, thereby generating the prediction image. a difference calculation unit for calculating a difference image between the intra-prediction image and a motion compensation image corresponding to the intra-prediction image; a low-pass filter unit for applying a low-pass filter to the difference image, thereby arriving at an image obtained by applying the low-pass filter by using the low-pass filter unit, a first gain adjustment unit for adjusting a gain of the image obtained by applying the low-pass filter by multiplying the image obtained by applying the low-pass filter with a first constant factor, thereby arriving at a first gain-adjusted image; high-pass filter unit for applying a high-pass filter to the image obtained by applying the low-pass filter by using the low-pass filter unit, thereby arriving at a filtered image, a second gain adjustment unit for adjusting a gain of the filtered image obtained by applying the high-pass filter by multiplying the filtered image obtained by applying the high-pass filter with a second constant factor, thereby arriving at a second gain-adjusted image; a first adding unit for adding the first and second gain-adjusted images, thereby arriving at an image obtained by addition; and a second adding unit for adding the image obtained by addition to the intra-prediction image generated by the intra-prediction image generating unit, thereby generating the prediction image.