In this paper we propose a new frame rate up conversion scheme which is used to overcome the motion blur problem of liquid crystal display caused by its slow response. The conventional bilateral motion estimation method which is mainly used in the frame rate up conversion scheme has a drawback that it cannot find true motion vector if there are blocks with simple texture in the search range. To solve this problem, a texture adaptive bilateral motion estimation method that increases cost value of block with simple texture is proposed. Also a motion estimation scheme that utilizes neighboring motion vector effectively is proposed to reduce computation time required to estimate motion. Since the proposed scheme does not apply all available motion vectors within the search range, the execution time of frame rate up conversion can be reduced dramatically. Experimental results show that the interpolated frame image quality of the proposed method is improved in subjective as well as objective view point compared with that of the conventional method.