A moving image encoding apparatus, which divides moving image data into a plurality of sub-data, encodes the sub-data in parallel by using a plurality of encoders, and thereafter splices the resulting encoded sub-bitstream data into a single bitstream, includes a convergence target deriving function for determining a target value for a first amount of buffer occupancy so that the first amount of buffer occupancy at a point in time at which data corresponding to a last picture contained in first sub-bitstream data is removed from a first hypothetical buffer does not drop below a second amount of buffer occupancy which represents the amount of space that second sub-bitstream data occupies in a second hypothetical buffer at that point in time.