1. A moving image encoding device comprising: a processor; a region division unit executable by the processor to divide an input image into a plurality of input image regions; a memory in communication with the processor and configured to store a plurality of already reproduced images as reference images; a motion estimation unit executable by the processor to search for a region having a determined level of correlation with a target region included in the input image, the region being a processing target included in a plurality of reference regions from the reference images stored in the memory, the motion estimation unit further executable by the processor to produce a motion vector of the target region; a prediction signal generation unit executable by the processor to produce a prediction signal of the target region based on a reference frame number of the target region specifying a reference image included in the reference images that is searched by the motion estimation unit, and the motion vector specifying a spatial positional relationship between the target region and a searched region of the reference image; a motion vector prediction unit executable by the processor to produce a prediction motion vector from one or more encoded motion vectors, and to produce a difference motion vector indicative of a difference between the motion vector produced by the motion estimation unit and the prediction motion vector; a residual signal generation unit executable by the processor to produce a residual signal indicative of a difference between the prediction signal of the target region and a target pixel signal of the target region; an encoding unit executable by the processor to encode the residual signal, the reference frame number, and the difference motion vector produced by the motion vector prediction unit; and a restoration unit executable by the processor to decode the encoded residual signal, and thereafter add the decoded residual signal to the prediction signal to produce a reference image, the restoration unit further executable by the processor to store the reference image in the memory; wherein the motion vector prediction unit is further executable by the processor to select a first region from previously encoded regions, and in response to the selected first region not having a reference frame number, or the reference frame number of the target region and the reference frame number of the first region being different, the motion vector prediction unit is further executable by the processor to search for and select a second region instead of said first region, said second region being selected from a search region established within said previously encoded regions based on a scaled form of the prediction motion vector, said second region selected due to having a determined level of correlation with a template region, the template region located around the target region and being composed of pixel signals already reproduced from the reference image specified with the reference frame number of the target region; and the motion vector prediction unit is further executable by the processor to produce the prediction motion vector based on a spatial positional relationship between the template region and the first region, or produce the prediction motion vector based on a spatial positional relationship between the template region and the second region, when the second region is selected by the motion vector prediction unit.