A corresponding MB2 for the left sequence is determined from the parallax vector of a coding-object MB1 of the frame Bi for the right sequence. The motion vector {circle around (2)} of the corresponding MB2 is used as an origin of the search area for finding the motion vector of the coding-object MB1. As an alternative, the motion vector {circle around (3)} of MB3 adjacent to the coding-object MB1 is used as an origin of the search area for finding a motion vector of the coding-object MB1. As another alternative, the motion vector {circle around (2)} or {circle around (3)}, whichever is higher in utility evaluation, is used as an origin. As a result, both the search area and the circuit size for detecting a motion vector can be reduced. This configuration provides a stereo video data motion vector coding apparatus small in circuit size and capable of detecting a motion vector with high accuracy.