1. A motion estimation apparatus which considers a correlation between blocks, comprising: a full search unit to divide a current frame/field into blocks of a predetermined size, and estimate an arbitrary motion vector of each block by a full search algorithm; a candidate motion vector estimating unit to compute a plurality of motion prediction error values by applying a block matching algorithm (BMA) to a current block of the blocks for motion estimation, and estimate at least one candidate motion vector from the motion prediction error value below a predetermined threshold, for motion compensation of the current block; and a motion compensating unit to compute a correlation between the respective candidate motion vectors and the motion vectors of adjacent blocks which are adjacent to the current block, and compensate one among the candidate motion vectors to a final motion vector of the current block based on the computed correlation.