1. An image encoding device comprising: an intra predictor for, when a coding mode corresponding to one of coding blocks into which an inputted image is divided is an intra coding mode, carrying out an intra-frame prediction process on each block which is a unit for prediction of the coding block to generate a prediction image; and an encoder for encoding coding mode information and an intra prediction parameter indicating an average prediction, wherein when the intra predictor carries out the average prediction, the intra predictor carries out a filtering process on target pixels of the intra prediction located at an upper end and a left end of the block, the filtering process using an intermediate prediction value, which is an average value of adjacent pixels of the block, and at least one adjacent pixel of the target pixel, and wherein the intra predictor sets a filter coefficient to ½, associated with the intermediate prediction value for a target pixel at an upper left corner of the block, and sets a filter coefficient to ¼, associated with an adjacent pixel adjacent to an upper side or a left side of the target pixel.