1. A method, implemented on an apparatus configured to compensate motion prediction, of compensating motion prediction relative to each of a plurality of motion compensating blocks formed by dividing an objective frame image of successive frame images using a plurality of reference frame images, while sequentially changing pixel-based sizes of the plurality of motion compensating blocks, the method comprising: thinning out, at the apparatus, pixels of a motion compensating block having a greatest pixel-based size to be taken as an uppermost layer of among blocks with smaller pixel-based sizes, each different pixel-based size of a block corresponding to a different layer of a frame image, to generate a size-reduced block in a lower layer having a predetermined size-reduction ratio; determining, at the apparatus, motion vector search ranges respectively within the plurality of reference frame images based on a plurality of size-reduced reference images reduced in size corresponding to the size-reduction ratio of the size-reduced block by detecting motion vectors respectively within the plurality of size-reduced reference images and increasing a size of the motion vectors by linear interpolation to provide motion vector search ranges with respect to the plurality of reference frame images which correspond to an increased size of the motion vectors, wherein for each layer of a frame image except a lowermost layer, motion vectors are detected within a search range which includes a plurality of peripheral pixels in a rectangular range having apexes corresponding to start and end points of a motion vector detected in a lower layer; and detecting, at the apparatus, an optimal motion vector while sequentially changing the pixel-based sizes of the plurality of motion compensating blocks, using each of the motion vector search ranges determined in the determining motion vector search ranges, by taking the motion compensating block having the greatest pixel-based size and performing a plurality of separate and independent sequences of incrementally dividing the motion compensating block having the greatest pixel-based size into smaller regions, and applying a size-reduced motion vector search range which is based on the motion vector search ranges to each of the smaller regions, each sequence dividing the motion compensating block having the greatest pixel-based size into different smaller regions than each of the other sequences and each of the sequences is performed substantially simultaneously to each other.