A median filtering apparatus and method for removing noise and improving an image quality with respect to all types of input images are provided. The median filtering apparatus may receive an input of N pieces of data, may form a data set including the N pieces of data, may calculate a difference array having an N×N size based on the N pieces of data in the data set, may sum component values for each column of the difference array, and may calculate an index of a column having a smallest value among sum values that are obtained by the summing operation and that are greater than or equal to a preset value.