1. An image coding apparatus which codes a current image using motion estimation, said image coding apparatus comprising: a search range control unit configured to set, as a search range for use in motion estimation, a search range that requires a transfer amount smaller than a first threshold value, the transfer amount being an amount of data to be transferred for use in motion compensation in decoding the coded image; an obtaining unit configured to obtain, in the motion estimation, pixel data of pixels within the set search range from an image storage unit configured to store a reference image including the pixels having the pixel data; and a motion estimation unit configured to perform the motion estimation using the obtained pixel data and pixel data of current pixels to be coded.