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 values below a predetermined threshold, for motion compensation of the current block; and a motion compensating unit to compute a correlation between the at least one candidate motion vector and the arbitrary motion vectors of adjacent blocks which are adjacent to the current block, and compensate the at least one candidate motion vector to a final motion vector of the current block based on the computed correlation.