1. A video encoding apparatus comprising: an intra-predictor configured to predict pixels of a current block by using pixels of a neighboring block to generate an intra-predicted block of the current block, the neighboring block being adjacent to the current block, and selectively perform a filtering on the intra-predicted block based on a correlation among values of pixels of the intra-predicted block to generate a predicted block of the current block; a subtractor configured to subtract the predicted block from the current block to generate a residual block; a transformer and quantizer configured to transform and quantize the residual block to generate a transformed and quantized residual block; and an encoder configured to encode the transformed and quantized residual block, wherein the filtering is not performed when the correlation is smaller than a threshold, and the threshold is determined based on a quantization parameter.