In this article, we propose a new frame rate up-conversion (FRU) method for temporal quality enhancement. The proposed FRU algorithm employs gradual and adaptive motion estimation based on confidence priority for selecting more accurate motion vectors (MVs). In order to estimate accurate MVs, we adaptively alternate a search range and the order of blocks to be searched depending on the confidence level in hierarchical motion estimation. The precedence of the proposed algorithm is conducted based on the confidence level that is decided by the complexity of pixel values in a block. In addition, we perform bi-directional motion compensation and spatial linear interpolation to fill occlusion regions. In our experiments, we found that the proposed algorithm is about 2 dB better than several conventional methods. Furthermore, block artifacts and blur artifacts are significantly diminished by the proposed algorithm.