Initial value is selected when motion estimation is performed using predicted motion vector in video codec in which multiple references are allowed, and coding amount of motion vectors is reduced using predicted motion vector. Motion vector encoding apparatus includes predicted motion vector generator that generates adjacent motion vectors of current block with respect to each of reference pictures and generates each predicted motion vector of the current block from the generated adjacent motion vectors, motion estimator that determines final motion vector of the current block and final reference picture corresponding to the final motion vector with regard to search regions of the reference pictures, differential unit that obtains difference between the final motion vector of the current block and final predicted motion vector corresponding to the determined final reference picture among the predicted motion vectors, and unit for encoding information about the final reference picture and the difference.