A motion video encoding apparatus includes: a group determining unit which determines, for each block, a group to which the block belongs; a group decode time information computing unit which computes a decode time for each group; a code amount control unit which controls, for each group, an amount of code resulting from entropy encoding each block in the group so that data needed for decoding all of the blocks in the group arrives at a stream receive buffer by a decode time of the group when the data is transmitted at a prescribed transmission rate; a compression unit which compresses the data of each block based on the amount of code of the block; an entropy encoding unit which entropy-encodes the compressed data of each block; and a decode information appending unit which appends, to data to be output, correction information for the decode time of each group.