A motion estimation apparatus and a method considers a correlation between blocks. The motion apparatus includes a full search unit which divides a current frame/field into blocks of predetermined size and estimates an arbitrary motion vector of each block by a full search algorithm; a candidate motion vector estimating unit which computes a plurality of motion prediction error values by applying a block matching algorithm (BMA) to a current block and estimates candidate motion vectors from motion prediction error values below a predetermined threshold; a motion compensating unit which computes a correlation between respective candidate motion vectors and the motion vectors of adjacent blocks and compensates one among the candidate motion vectors to a final motion vector of the current block based on the computed correlation. By estimating motion vector of the current block in consideration of the correlation between the blocks, images free of block artifact can be provided.