A method and apparatus are provided for improving the compression efficiency of motion vectors of an unsynchronized picture by efficiently predicting the motion vectors using motion vectors of a lower layer. The method compresses motion vectors of an unsynchronized picture belonging to a current layer in a video encoder based on a multilayer having at least the current layer and a lower layer of the current layer. The method includes selecting a base picture for the unsynchronized picture, generating a predicted motion vector of the current layer from a motion vector of the base picture, subtracting the predicted motion vector from a motion vector of the unsynchronized picture, and encoding the result of subtraction.