The classical dark channel prior defogging algorithm easily loses image details. Alternatively, the defogging algorithm based on edge-preserving filtering can effectively protect image details; however, it is time-consuming. Aiming at the aforementioned problems, this paper proposed an adaptive exponentially weighted moving average filtering algorithm that protected image edge details while taking less time. Combined with an improved dark channel, this method achieved fast and precise defogging. First, the improved dark-channel algorithm was applied to obtaining a rough distribution of atmospheric transmittance. Second, the transmittance was optimized by employing the adaptive exponentially weighted moving average filtering algorithm. Subsequently, the transmittance of the bright region was repaired to avoid color distortion. Finally, the defogged image was processed using the transformation of the atmospheric scattering model. The experimental results show that the proposed algorithm has a high execution speed; moreover, the defogged image processed using the proposed algorithm has good performance under the following three nonreference objective evaluation indexes: effective edge intensity, color reproduction ability, and structural information.