1. A method performed by an apparatus for decoding an image, the method comprising: restoring a residue by entropy-decoding a received bit stream and by performing inverse quantization and inverse transform on the residue; generating a prediction unit by performing intra-prediction that selectively uses one of a plurality of prediction modes; and restoring the image by adding the residue to the prediction unit, wherein when a planar intra prediction mode is activated, a predicted pixel value of an internal pixel of a current prediction unit is obtained by performing bilinear interpolation using (i) vertically and horizontally directional corresponding pixel values in previously decoded left side block and upper end block of the current prediction unit, and (ii) vertically and horizontally directional corresponding internal boundary prediction pixel values in the current prediction unit, wherein the vertically and horizontally directional corresponding pixel values in the previously decoded left side block and upper end block of the current prediction unit include: a pixel value of a third pixel which is located on a lowermost boundary of the upper end block of the current prediction unit and on the same vertical column as the internal pixel, and a pixel value of a fourth pixel which is located on a rightmost boundary of the left side block of the current prediction unit and on the same horizontal row as the internal pixel.