A motion estimation method capable of setting an optimum threshold value and allowing high speed processing includes the steps of: sequentially selecting one of blocks to be searched from a search range; sequentially calculating a difference between corresponding sample values of a reference block and one of blocks to be searched and accumulating an absolute value of difference; comparing an intermediate result of an accumulation value and a prescribed threshold value for a prescribed number of samples and interrupting the step of accumulating the absolute value of difference when the intermediate result exceeds the prescribed threshold value; and making one of blocks to be searched having a minimum final result of the accumulation value correspond to the reference block. The prescribed threshold value is dependent on the reference block. It is noted that the motion estimation apparatus is also disclosed.