An intra prediction encoding apparatus includes: an optimal filter selecting unit for providing a plurality of extrapolation prediction filter candidates for filtering pixels adjacent to a current block to be encoded, with respect to each intra prediction direction or prediction mode of the current block, and selecting a filter having lowest encoding cost among the plurality of extrapolation prediction filter candidates; a residual signal generating unit for generating an extrapolation prediction value of the current block through the filter selected by the optimal filter selecting unit, and generating a residual signal by calculating a difference between a generated extrapolation prediction value of the current block and a pixel value of the current block; a transform and quantization unit for performing transform and quantization on the residual signal generated by the residual signal generating unit; and an entropy encoding unit for performing entropy encoding on a transformed and quantized residual signal.