A video encoding/decoding apparatus includes a video encoder and a video decoder. The video encoder is configured to set up motion vector resolutions differentiated by search areas centered on a prediction motion vector of a current block, perform a motion estimation with a resolution corresponding to each of the search areas to generate a motion vector, and encode a differential motion vector between the generated motion vector and the prediction motion vector. The video decoder is configured to extract the differential motion vector from a bitstream, and decode the extracted differential motion vector with a resolution corresponding to a search area where the differential motion vector belongs to among the search areas.