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 only on target pixels of the intra prediction, wherein the target pixels consist of pixels located at an upper end and pixels located at a left end of the bock, 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.