To provide an image encoding device and an image decoding device which can reduce the calculation amount at the time of generating a plurality of encoding streams of different frame rates concurrently with a low memory amount.

When a motion vector detected by a motion search in the generation of a first encoding stream is used in succession in the generation of a second encoding stream, the motion vector in the first encoding stream is selectively stored; a block in which a motion vector is stored corrects the stored motion vector for use in the generation of the second encoding stream; and a block in which the motion vector is not stored uses a motion vector calculated by prediction from a peripheral block.