An apparatus for improving fogged image using user-controllable root operator comprises an atmosphere brightness value calculation unit for receiving a fogged input image and calculating the value of the brightest pixel of the atmosphere, a transmission calculation unit for calculating the lower bound of transmission rate by using the pixel value calculated by the atmosphere brightness value calculation unit and the fogged input image, and calculating the transmission rate for each pixel by computation processing of power operation with the lower bound of transmission rate according to the user control value, a restoration image computation unit for outputting restored image in which the fog is removed by using the transmission rate calculated by the transmission rate computation unit and the fogged input image, and a post-processing unit for outputting a fog-eliminated image by performing brightness stretching or color processing.