In this paper an adaptive moving method of the search region tracking the motion is proposed. The search region in BMA is determined by the capability of hardware implementation and the degree of motion. But once determined nothing can be changed during coding procedure. In this paper we predict the level of motion of the current block using motion vectors of previous frames without overhead information and change the location of the search region according to the level of the motion predicted. In short the proposed method can be archieved the dsirable effect such that the size of search region gets large when the motion is large. Results of experiments show that prediction efficiency has been improved by using adaptive moving method resulting in reduced prediction error in the blocks with large motion.