A display apparatus and method that reduces block noise by performing block noise boundary detections and generating a block noise boundary map on the basis of a result of the detections to cope with local random block noise having irregular shaped and blurred block boundaries to perform adaptive deblocking filtering. The apparatus includes: an image receiver; a map generator to generate a block boundary map by performing convolution using a plurality of kernels on a received image; a determiner to determine a filter parameter on the basis of the block boundary map and a block boundary period included in the block boundary map; a deblocking filter to vary a filter strength on the basis of the determined filter parameter; and a display on which an image in which block noise is removed by the deblocking filter is displayed.