A residual picture is produced and encoded that is a residual picture that is a residual signal between a picture to be coded that is an input moving-picture video signal to be subjected to coding and a predictive picture produced from a reference picture that is a local decoded video signal for each of a plurality of rectangular zones, each composed of a specific number of pixels, into which a video area of the moving-picture video signal is divided. A boundary condition of each of a plurality of borders is obtained between the rectangular zones and another plurality of rectangular zones adjacent to the rectangular zones, and a border, of the reference picture, having a boundary condition that matches the boundary condition, is found by motion-vector search in the reference picture, and border motion-vector data is generated that is data on a motion vector from a border of the rectangular zone in the picture to be coded to the border of the reference picture thus found. A boundary condition of a border that corresponds to the border motion vector data is defined from the reference picture based on the border motion-vector data, and an estimated video signal is generated in each rectangular zone in the picture to be coded, that satisfies Poisson's Equation, thus producing a first predictive picture. The residual picture is then produced with the first predictive picture as the predictive picture and encodes the residual picture.